5. Find the average value of the function on the given interval. (a) f(x) = x²-4x+3, [0,3] (b) f(x)=8 cosx-sec² x, ππ 3'3

Q: 10. (a) State the Fundamental Theorem of Calculus. -x sin t %3D (b) Let J(x) = S*. Evaluate: (i)…

A: Fundamental theorem of calculus

Q: Given the function fx)=x cosx. Use the centered-divided-difference formula f '(x) = 2h to compute…

A: We will use center difference formula  f'(x)=f(x+h)-f(x-h)2h

Q: Find the derivative of the function.

A: y=1212lnx+1x-1+arctanx⇒y=1212lnx+1-lnx-1+arctanx    ∵lnxy=lnx-lny⇒y=1212lnx+1-12lnx-1+arctanx

Q: Find the x values of all the horizontal tangents to the function f(x) = cos.x + /3 sinx on the…

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Q: 3. Use the second derivative test to find the local extrema of f(x) = cos x + sin x on the interval…

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Q: (c) Differentiate the following functions with respect to x. (i) х3 + 5y4 — 2 — 1. (ii) y = -…

A: Differentiate the given functions with respect to x.

Q: a) Differentiate the function below with respect to x. 3+7x –3–52 f(x) = 33

A:

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: 11. Estimate the approximate derivative of f(x) = sin²(x) at x = 0.45 radian, for h = 0.05 and 0.1…

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Q: Compute the first and second derivatives of the functions: 1.) y=tan(x/3) at x = 3

A: Given; y=tan(x/3) at x=3.

Q: Find the derivative of the following functions without skipping steps w = 7x sin (z?) – z? sin (y) +…

A:

Q: Sx2 - 1 x > 1 (1- x, x < 1' 3. Show that the function f (x) = has no derivative at x = 1.

A:

Q: x + 2x sin 01: Let f(x)={ . Find f'(0) if it exists. ,x= 0

A:

Q: Find all the values of r for the given function defined by y = r³ – 12x where the tangent line is…

A:

Q: H. For the function f(x)= cos(ax), find all MVT Values 0<c <2 where f(2)-f(0)= f'(c)(a - o)

A:

Q: The forward difference approximation to the derivative f(x) = x² sin(2x) at x = π/3 is: (use step…

A: The forward difference approximation to the derivative f(x) = x2 * sin(2x) at x= π/3 (use step size…

Q: Find the derivative of (a) f(z) = (z+4 sin z) (1-7 cos z), and %3D sin z (b) g(z)

A: Part (a) Given function is fx=x+4sinx1-7cosx

Q: C. Solve the following problem. 1.) Find (fg)' if f(4) = 3, f'(4) = 2 , g(4) = -6, and g'(4) = 8.…

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Q: i) Consider f(x) = x² – 3x . a. Find f(2) . b. Determine f'(x). c. Find f'(2) .

A: Hi, As given are multiple questions, according to the Bartleby rules we are supposed to do 3 sub…

Q: x2 1)Calculate the derivative using FTC(1): g(x) = ʃ  (t5 − 9t3 )dt…

A: 1) to find the derivative of the integral using FTC(1)

Q: 3V3 Let f(r) = sin (2r) so that f () = 2 0.6495 (a) Find linear function for the tangent line to y =…

A:

Q: 1/2 105. Show that f (sin 0) de = f (u)- 1-и2 du.

A:

Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

A: