A(x) = 22 -2 f(t)dt.

Q: Restrict the domain of f(z) such that it is one-to-one (if it wasn't already), and then sketch the…

A: Horizontal line test: If the horizontal line intersects the graph of a function in all places at…

Q: (a) F(3) = (b) F'(3) = (c) F"(3)

A:

Q: Let F(x) = dt. Then %3D 25 (t + t10)15 F'(x) = %3D

A:

Q: i(t) = (A₂ + A₁t)e-at

A:

Q: d (F(x*) dt dx dx

A: Explanation of the answer is as follows

Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

A:

Q: dx Determine x = f(t) for (t² +8t) - x = f(t) = dt = 8x+8, t>0; f(1) = 3.

A:

Q: Use definition find L{3t} 8 -Sª L{f(t)} = e-st f(t) dt to

A:

Q: dP Pt, P(1) = 3 %3D dt

A:

Q: Find the average rate of change of f(x)=−x2+9x on the interval [1,6].

A: Given: The given function is, f(x) = -x2 + 9x  on [1, 6]   To determine: The average rate of change…

Q: 1 Find f(1) if f(t) dt = x" - x + 2x? – 2, x >1.

A:

Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: When is f (t) increasing at the greatest rate?

A:

Q: r| f(x)dx = 45, then

A:

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: r(a) e-t ta-1 dt

A:

Q: F(x) = 9t dt

A: given: Fx=∫0x29t dt Fx=∫0x29t dt=9∫0x2t dt=9t1+11+10x2=9t220x2=92t20x2=92x22-02=92x4-0=92x4

Q: f(x) dx = 18 and f(x) dx = 3.7, find f(r) dr.

A: using property of definite integration

Q: t² - t dt 0, = (x)6 g'(4) =

A:

Q: g(x) g'(5) = 2 X 13 1+t2 dt

A: Given query is to find indicated derivative.

Q: (f) ef +1 ex dx

A:

Q: P. (F(2³)) dz 13

A: We have to find derivative

Q: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

Q: dy = 4x -3 and y(4) = 0. dx Find the function y(x) satisfying

A: