Someone please help with all of the above questions?? with complete steps. I hav

Question

Someone please help with all of the above questions?? with complete steps. I have a quiz tomorrow... Thank you.

In-Class Problems Applied Calculus I Spring 2017 1. (1/11) If f(a) -a 2 2r, find f (a h) f (a) and simplify your answer G. Express your answer in interval 2. (1/13) Find the domain of the function f(z) notation 3. (1/18) A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 30 e ft2, the material for the sides costs 10 e/ft2, and the material for the top costs 20 e/ft Letting denote the length of one side of the base, find a function in the variable a giving the cost (in dollars) of constructing the box. 4. (1/20) Find the indicated limit. lim 5. (1/23) Evaluate the limit, if it exists. 6. (1/25) Find lim f(a) and lim f(r), Where 1 1 if r f(a) if 1 1 f 1 Determine whether f is continuous at r 1 or not. Justify your answer 7. (01/27) In which one of the given intervals does the function f have a real root? Please justify your answer using the Intermediate Value Theorem. f(z) (a) (-1,0) (b) (0,1) (c) (1,2 (d) (2,3) (e) no roots exist. S. (1/30) If f (ar) 3r, then find the slope of the tangent line to the graph of f at any point by using the following for f'(r) lim 9. (2/1) Find the derivative of the function f by using the rules of differentiation 10. (2/3) Find an equation of the tangent line to the graph of the function f(a) 3r 1 at the point where a 11. (2/3) Let f(r) 2 3 12a: 6. Find the values of r for which f (a) -0.

Explanation / Answer

1. f(x)=-x2+2x

f(a+h) - f(a)= -(a+h)2+2(a+h)+a2-2a

= -a2-h2-2ah +2a+2h +a2-2a

= -h2-2ah +2h=-h(h+2a-2)

2. f(x)= x/(x2-x-6) = x/(x-3)(x+2)

Its a rational expression and in rational expression denominator must be not equal to zero

And at x=-2 or x=3 ,denominator becomes zero

Hence domain is (-infinity,-2)U(-2,3)U(3,infinity)

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