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Let f(x) = 1/x + 3 Use the limit definition of the derivative to find To avoid c

Let f(x) = 1/x + 3 Use the limit definition of the derivative to find To avoid calculating four separate limits: I suggest that you evaluate the derivative at the point when x = a…

Let f(x) = 1/x^2 on the interval (0, infinity). Using the definition of the deri

Let f(x) = 1/x^2 on the interval (0, infinity). Using the definition of the derivative, find f'(c) for c>0. **definition of derivative: Let f: A --> R be defined on an inter…

Let f(x) = 2 + 2x2 - x2 Find the horizontal and vertical asymptotes of the graph

Let f(x) = 2 + 2x2 - x2 Find the horizontal and vertical asymptotes of the graph of f(x). Determine intervals on which f is increasing and intervals on which f is decreasing. Also…

Let f(x) = 2(x - 4)2/3 + 2. Find all critical values and list them below. Note:

Let f(x) = 2(x - 4)2/3 + 2. Find all critical values and list them below. Note: If there are no critical values, enter 'NONE'. Use interval notation to indicate where f(x) is incr…

Let f(x) = 2x2 -11x + 2 The slope of the tangent line to the graph of f(x) at th

Let f(x) = 2x2 -11x + 2 The slope of the tangent line to the graph of f(x) at the point (2, -12) is The equation of the tangent line to the graph of f(x) at (2, -12) is y = mx + b…

Let f(x) = 2x^2 + 3x + 1 and h (x) = 2 (-x)^2 + 3 (-x) + 1. The graph of h can b

Let f(x) = 2x^2 + 3x + 1 and h (x) = 2 (-x)^2 + 3 (-x) + 1. The graph of h can be derived from the graph of f by: Shifting the graph of f to the left one unit Shifting the graph o…

Let f(x) = 2x^2 - 3x + 1. Find and simplify f(a + h) - f(a)/h (h notequalto 0).

Let f(x) = 2x^2 - 3x + 1. Find and simplify f(a + h) - f(a)/h (h notequalto 0). Answer: ______ The average number of email messages sent and received per corporate user per day in…

Let f(x) = 2x^2 - 4x. show your work to justify all solutions a. Find the avg. r

Let f(x) = 2x^2 - 4x. show your work to justify all solutions a. Find the avg. rate of change of f over the interval [3,3+h]. How is this related ot the secant line passing throug…

Let f(x) = 3 x^2 + 5x. Find a simplified formula for the average rate of change

Let f(x) = 3 x^2 + 5x. Find a simplified formula for the average rate of change f(x + h0 - f(x)/h Suppose a colony of bacteria is known to grow exponentially with time. At the of …

Let f(x) = 3e^cos(x). The graph of f and its first four derivatives on [2, 7] ar

Let f(x) = 3e^cos(x). The graph of f and its first four derivatives on [2, 7] are shown on the next page. (Be careful when examining the graphs; look carefully at the vertical sca…

Let f(x) = 3x2 / 3 - x2. Find all critical points of f(x). Classify these critic

Let f(x) = 3x2 / 3 - x2. Find all critical points of f(x). Classify these critical points into local minimum using the first derivative test.

Let f(x) = 4x^2 - 3x + 2. Recall the derivative of f at x = a, which is denoted

Let f(x) = 4x^2 - 3x + 2. Recall the derivative of f at x = a, which is denoted by f'(x). is the slope of the tangent line to the graph of y = f(x) and. in terms of the limits of …

Let f(x) = 4x^3 ? 9. Find the open intervals on which f is increasing (decreasin

Let f(x) = 4x^3 ? 9. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). f is increasing on the interv…

Let f(x) = 8x2 - 5x and g(x) = 7x + 9. Find composite g[f(-k)] 392k2 + 973k + 60

Let f(x) = 8x2 - 5x and g(x) = 7x + 9. Find composite g[f(-k)] 392k2 + 973k + 603 392k2 - 973k + 603 56k2 + 35k + 9 56k2 - 35k + 9 Find functions f and g such that y = f(g(x)). y …

Let f(x) = 9x^2 - 4x + 1/x - 3/x^2 + 8. Suppose that F(x) is an antiderivative o

Let f(x) = 9x^2 - 4x + 1/x - 3/x^2 + 8. Suppose that F(x) is an antiderivative of f(x) such that F(1) = 22. Find F(x). A can of soda that had left in the sun is placed in a cooler…

Let f(x) = COS (ax) on the interval [3pi / 2a, 7pi / 2a]. where a > 0. List crit

Let f(x) = COS (ax) on the interval [3pi / 2a, 7pi / 2a]. where a > 0. List critical points in order from smallest (A) to largest (B). A: B: For what x is f?(x) = 0 on (3pi / 2…

Let f(x) = e^x +3x. A student was asked to show why there was a root c in the in

Let f(x) = e^x +3x. A student was asked to show why there was a root c in the interval [1.0,0]. The student responded with the following argument: First we must calculate the valu…

Let f(x) = ex for -1 le x le 1. Write a Matlab program that interpolates f at n

Let f(x) = ex for -1 le x le 1. Write a Matlab program that interpolates f at n + 1 points with a polynomial p of degree n or less, for each of the following cases. n + 1 evenly s…

Let f(x) = log_a(x), use words to describe each of the following transformations

Let f(x) = log_a(x), use words to describe each of the following transformations: (a) g(x) = 4 - 5 f(x-2) (b) h(x) = f(3x) - 6 Solve for x if log (x^2-49)-log(x+7) = 1 If log_b x=…

Let f(x) = p(x)/h(x), where p(x) is a ppolynomial of degree a and h(x) is a poly

Let f(x) = p(x)/h(x), where p(x) is a ppolynomial of degreea and h(x) is a polynomial of degree b. Complete each statement with an equal sign or an inequalitysign. a) f(x) has a h…

Let f(x) = x + 2/x - 3. Find f^-1 (-1). a. 1/2 b. -1/2 c. 3 d. -5/2 e. undefined

Let f(x) = x + 2/x - 3. Find f^-1 (-1). a. 1/2 b. -1/2 c. 3 d. -5/2 e. undefined Let f(x) = 1/x. Find f(x+h)-f(x)/h. a. f(x) = h/x(x+h) b. f(x) = 1/x^2 c. f(x) = -1/x(x+h) d. f(x)…

Let f(x) = x 4 +x 2 -6 . Findthe zeros of f(x) and choose the appropriaterespons

Let f(x) = x4+x2-6 . Findthe zeros of f(x) and choose the appropriateresponse. A. f(x) has no real zeros B. f(x) has exactly 1 real zero C.  f(x) has exactly 2 real zeros D. f(x) …

Let f(x) = x4-50x2/12. Use the definition of a derivative or the derivative rule

Let f(x) = x4-50x2/12. Use the definition of a derivative or the derivative rules to find f'(x) = Use the definition of a derivative or the derivative rules to find f''(x) = On wh…

Let f(x) = x^3 + 2x^2 + 7x - 11 and g(x) = f(x - 4). Which of the following desc

Let f(x) = x^3 + 2x^2 + 7x - 11 and g(x) = f(x - 4). Which of the following describes g as a function of f and gives the correct rule? horizontal compression; g(x) = 4x^3 - 40x^2 …

Let f(x) = x^3 - 12r^2 + 45x + 14. Find me open Intervals on which f is increasi

Let f(x) = x^3 - 12r^2 + 45x + 14. Find me open Intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). f is increasing …

Let f(x) = x^3 - 5x^2 + 2x-7 and g(x) = f(4x). Which of the following describes

Let f(x) = x^3 - 5x^2 + 2x-7 and g(x) = f(4x). Which of the following describes g as a function of f and gives the correct rule? vertical stretch; g(x) = 4x^3- 20x^2 + 8x - 28 ver…

Let f(x) = x^3 -3x^2 - 1, x greaterthanorequalto 2. Find the value of df^-1/dx a

Let f(x) = x^3 -3x^2 - 1, x greaterthanorequalto 2. Find the value of df^-1/dx at the point x = -1 f(3). Let f(x) = x^2 -4x -5, x > 2. Find the value of df^-1/dx at the point x…

Let f(x) = x^4 - 72 x^2/7 (a) Use the definition of a derivative or the derivati

Let f(x) = x^4 - 72 x^2/7 (a) Use the definition of a derivative or the derivative rules to find f'(x) = (b) Use the definition of a derivative or the derivative rules to find f"(…

Let f(x) = xe^x. For what values of x is the graph of f both decreasing and conc

Let f(x) = xe^x. For what values of x is the graph of f both decreasing and concave up? Explain your reasoning using algebra. Please showcorrect work for full rating.

Let f(x) = {- 4/x + 3 if x - 3 Calculate the following limits by using a graph o

Let f(x) = {- 4/x + 3 if x - 3 Calculate the following limits by using a graph or a table of values. Enter "DNE" NOT "infinity" if the limit does not lim_x rightarrow - 3 f(x) = l…

Let f(x) be a continuous function and consider the integration of f(x) from x =

Let f(x) be a continuous function and consider the integration of f(x) from x = a to x = b where b > a. It is easily shown using the basic definition of the Riemann integral (t…

Let f(x) be the function whose graph is shown below. Determine f\'(a) for a = 1,

Let f(x) be the function whose graph is shown below. Determine f'(a) for a = 1, 2, 4, 7. A laboratory study investigating the relationship between diet and weight in adult humans …

Let f(x)= sqrt (12+x) and g(x)= sqrt (12-x) a) the domain of f+g is b) the domai

Let f(x)= sqrt (12+x) and g(x)= sqrt (12-x) a) the domain of f+g is b) the domain of f-g is c) the domain of fg is d) the domain of f/g is note: each answer should be in interval …

Let f(x)= x - 3 + (2/x+1) determine the intervals where f(x) is increasing, inte

Let f(x)= x - 3 + (2/x+1) determine the intervals where f(x) is increasing, intervals where f(x) is decreasing, intervals where f(x) is concave up, concave down, all points whicj …

Let f(x)= x2- 7x+12 / x-a. Complete parts (a) through (c) below. a. For what val

Let f(x)= x2- 7x+12 / x-a. Complete parts (a) through (c) below. a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if nece…

Let f(x)=-x3+9x2-15x+ (a) Find the intervals where f is increasing and where f i

Let f(x)=-x3+9x2-15x+ (a) Find the intervals where f is increasing and where f is decreasing. (b) Find intervals where f is concave upward and where f is concave downward. (c) Fin…

Let f(x)=1x4 and g(x)=2x+4. Find the following functions. Simplify your answers.

Let f(x)=1x4 and g(x)=2x+4. Find the following functions. Simplify your answers. f(g(x))=     , g(f(x))=     . The function h(x)=(x+1)4 can be expressed in the form f(g(x)) where …

Let f(x)=5x^4-12x^3 a) find The x-coordinates of all critical points of f. B) fi

Let f(x)=5x^4-12x^3 a) find The x-coordinates of all critical points of f. B) find intervals of increase and intervals if decrease c) at which value of x have local max and mim Le…

Let f(x)=sec(x) Find the 2nd order polynomial of f at c=pi/4. Please show the ca

Let f(x)=sec(x) Find the 2nd order polynomial of f at c=pi/4.   Please show the calculation of the 2 derivatives using hand rules. Using the polynomial obtained above, approximate…

Let f(x)=x3 - V2x2 + 21x - 12. Use interval notation to indicate where f(x) is i

Let f(x)=x3 - V2x2 + 21x - 12. Use interval notation to indicate where f(x) is increasing. Note: Use 'INF' for infinity. '-INF' for - infinity. and use 'U' for the union symbol. I…

Let f(x)=xe^x A)Determine domain and range? B)Is f(x) an odd function, an even f

Let f(x)=xe^x A)Determine domain and range? B)Is f(x) an odd function, an even function ,or neither? Explain your answer using APPROPRIATE TESTS! C)Find the roots of f(x). DETERMI…

Let f(x)=xe^x A)Determine domain and range? B)Is f(x) an odd function, an even f

Let f(x)=xe^x A)Determine domain and range? B)Is f(x) an odd function, an even function ,or neither? Explain your answer using APPROPRIATE TESTS! C)Find the roots of f(x). DETERMI…

Let f(x, y) = x 2 + y 2 . (a) Using the method of Lagrange multipliers, optimize

Let f(x, y) = x 2 + y 2 . (a) Using the method of Lagrange multipliers, optimize f(x, y) with respect to the constraint x + y = 10. That is, find the point (x, y) satisfying the c…

Let f(x, y) = x2 + 3xy + 5y2 + 4x3 - y3. Use the second derivative test to decid

Let f(x, y) = x2 + 3xy + 5y2 + 4x3 - y3. Use the second derivative test to decide if the point (0.0) is a local minimum or local maximum or a saddle point. If the test is inconclu…

Let f(x, y) be a function of two variables x and y. We define the laplacian of f

Let f(x, y) be a function of two variables x and y. We define the laplacian of f to be the combination of derivatives 2f = 2f/ x2 + 2f/ y2 This operator is extremely useful in mod…

Let f(x, y, z) = x2y + z and r(t) = (e2t, 2, t2). Compute d/dt[f(r(t))] 4e2t + 2

Let f(x, y, z) = x2y + z and r(t) = (e2t, 2, t2). Compute d/dt[f(r(t))] 4e2t + 21 4e2t 8e4t + 2t 4xye2t + 2t 8e2t + x2 + 2t None of these What is the maximum value of f(x, y) = 4x…

Let f(x, y, z) = x^4 y^3 + z^2 and x = st, y = st^2, and z = st. (a) Calculate t

Let f(x, y, z) = x^4 y^3 + z^2 and x = st, y = st^2, and z = st. (a) Calculate the primary derivatives partial differential f/partial differential x = 4x^3y^3 partial differential…

Let f(x, y, z) = xy^3 + z^2 and x = s^3t^3, y = st^3, and z = s^2t^2 Calculate t

Let f(x, y, z) = xy^3 + z^2 and x = s^3t^3, y = st^3, and z = s^2t^2 Calculate the primary derivatives partial differential f/partial differential z = partial differential f/parti…

Let f(x, y. z) = x1 + xy + yz. Grading Policy: Points 7+7+2+2+2. Calculate Delta

Let f(x, y. z) = x1 + xy + yz. Grading Policy: Points 7+7+2+2+2. Calculate Delta (f)(l. 2,5). Grading Policy: gradient 4 and evaluation 3. Answer: Gradient = evaluates to . (b) Ca…

Let f(x,y) = 1 + x2 - cos(5y). Find all critical points and classify them as loc

Let f(x,y) = 1 + x2 - cos(5y). Find all critical points and classify them as local maxima, local minima, saddle points, or none of these. critical points: (give your points as a c…