Q1) ----------------------------------------------------------------------------

Question

Q1)

-------------------------------------------------------------------------------------------------------------------------------------

Q2)

-------------------------------------------------------------------------------------------------------------------------------------

Q3)

-------------------------------------------------------------------------------------------------------------------------------------

Q4)

-------------------------------------------------------------------------------------------------------------------------------------

Q5)

-------------------------------------------------------------------------------------------------------------------------------------

Q6)

-------------------------------------------------------------------------------------------------------------------------------------

Q7)

-------------------------------------------------------------------------------------------------------------------------------------

Q8)

Find the tangent line approximation for 9 + x near x = 0. 9 + x = Find the tangent line approximation to -- near x = 16. 16 /x= What is the local linearization of f(x) = ex near x = 1? Ex5 Find the tangent line approximation to cos(x) near x = pi/4. Is the tangent line approximation in part (a) an under-estimate or over-estimate for 0

Explanation / Answer

Q1)

f(x) = sqrt(9+x)

f(0) = sqrt(9) = 3

f'(x) = 1 / 2sqrt(9+x)

f'(0) = 1/6

T(x) = (1/6)x + 3

Q2)

f(x) = 16/x

f(16) = 16/16 = 1

f'(x) = -16/x^2

f'(16) = -16/16^2 = -1/16

T(x) = (-1/16)(x-16) + 1

Q3)

f(x) = exp(x^5)

f(1) = exp(1) = e

f'(x) = 5*x^4 * exp(x^5)

f'(1) = 5e

T(x) = (5e)(x-1) + e

Q4)

f(x) = cos(x)

f(pi/4) = 1/sqrt2

f'(x) = -sin(X)

f'(pi/4) = -sin(pi/4) = -1/sqrt2

T(x) = (-1/sqrt2)(x-pi/4) + 1/sqrt2

"Over-estimate because cos(x) is concave down on the interval"

Q5)

f(x) = exp(5x)+x

f'(0) = 1

f'(x) = 5exp(5x)+1

f'(0) = 5+1 = 6

T(x) = 6(x) + 1 = 2

6x = 1

x = 1/6

Q6)

T(5.1) = (-3.9)(5.1-5) + 17

= 16.61

Q7)

No idea.

Q8)

(a) f'(4) > f'(5)

(b) 0 is larger (because f''(4)<0)

(c) f(4)+f'(4)dx is larger (concave down = overestimation)

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.