Question

Question 11 (1 point) Let $f(x)$ be a function that is continuous for all $x$ and satisfies: $f(0) = 4$, $f(1) = 0$, $f(3) = 6$, $f(9) = 2$. Let $g(x) = \int_2^{\sqrt{x}} f(t) dt$. What is the value of $g'(9)$? 2 $\frac{1}{4}$ 1 $\frac{1}{8}$ 8 Question 12 (1 point) Evaluate $\int_0^{\sqrt{\ln(5)}} xe^{x^2} dx$. 2 $\frac{1}{5}$ 0 $\frac{1}{2} (e^{\ln(5)} - 1)$ $e^{\sqrt{\ln(5)}} - 1$

          Question 11 (1 point)
Let $f(x)$ be a function that is continuous for all $x$ and satisfies:
$f(0) = 4$, $f(1) = 0$, $f(3) = 6$, $f(9) = 2$.
Let $g(x) = \int_2^{\sqrt{x}} f(t) dt$. What is the value of $g'(9)$?
2
$\frac{1}{4}$
1
$\frac{1}{8}$
8
Question 12 (1 point)
Evaluate $\int_0^{\sqrt{\ln(5)}} xe^{x^2} dx$.
2
$\frac{1}{5}$
0
$\frac{1}{2} (e^{\ln(5)} - 1)$
$e^{\sqrt{\ln(5)}} - 1$

Question 11 (1 point)
Let f(x) be a function that is continuous for all x and satisfies:
f(0) = 4, f(1) = 0, f(3) = 6, f(9) = 2.
Let g(x) = ∫2^√(x) f(t) dt. What is the value of g'(9)?
2
(1)/(4)
1
(1)/(8)
8
Question 12 (1 point)
Evaluate ∫0^√(ln(5)) xe^x^2 dx.
2
(1)/(5)
0
(1)/(2) (e^ln(5) - 1)
e^√(ln(5)) - 1

Added by Cheryl L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Manisha Sarker

12/26/2022

Step 1

The fundamental theorem of calculus states that if F(x) is an antiderivative of f(x), then the definite integral of f(x) from a to b is F(b) - F(a). So, g'(x) = f(√(x)) * (d/dx)(√(x)) = f(√(x)) * (1/(2√(x))) Show more…

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Question 11 (1 point) Let f(x) be a function that is continuous for all x and satisfies: f(0)=4, f(1)=0, f(3)=6, f(9)=2. Let g(x)=∫(2 to √(x)) f(t) dt. What is the value of g'(9)? 2 (1)/(4) 1 (1)/(8) 8 Question 12 (1 point) Evaluate ∫(0 to √(ln(5))) x*e^(x^2) dx 2 (1)/(5) 0 (1)/(2)(e^(√(ln(5)))-1) e^(√(ln(5)))-1