13. Calculate each of the following Suppose that = 0.1 f(10t) dt = 0.25 f(1 4t) dt 0 0.5 f(2 4t) dt J0.25

Q: Find dy/dx

A: Using the second fundamental theorem of calculus and the chain rule we get

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

A:

Q: Let xy = 4 and dx dt Find dy dt when x = = 2. 1.

A: ..........(i)Differentiating equation with respect to t Put   ..........(ii)

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

A:

Q: Let x+y = 100,if dx dy = 2, find dt when y-6 and x-8 %3D

A:

Q: 11.6.49 The ellipse 25 = 1 is shifted up 6 units and left 7 units. Find an equation for the new…

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

A:

Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0

A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.

Q: dy If Vx +Vy=5 and dx - 3. find the value of when X=1 dt dt

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Q: Let f' (t) dt = 9 and f (2) = 3. Find f (6).

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Q: At a certain moment, the temperature in a snake cage satisfies dT /dt = 0.008◦C/s. Estimate the rise…

A: Given - Temperature in the snake cage is dTdt=0.008°C/s To find - the rise in temperature over the…

Q: = 1₁²₂ x 3. Define F(x): 1 /1+t² dt. Find F(8) and F'(8).

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: If f(x)dx = 32, then f(t)dt : %3|

A: Here, Order of limit has been exchanged with each other.

Q: What is the derivative of M(t) = 1.19t + 13.22

A: