24 8. (10) Let g(x) = sin (x) if a +0 %3D 0. if r=0 Is g' is continuous at 0?

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: Let f(x) 6 sin x + 4 cos z Then f'(x) = The equation of the tangent line to y = f(x) at a = π/3 can…

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Q: z + 2.5 -3 = Z

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Q: Is there a function f(x, y) such that fx : one. If not, explain the reason = e* cos y and fy : = e*…

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Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b)' y = e(4x+) e(tx+) X. c) y = e*(sin…

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: the line 3x+ y=l is the tangent line for the graph of y= f(x) at x=1, then f'(1)= 1 (C) 1 (D) 3 A) 3…

A: The slope of the line y=mx+c is m. The slope is equal to the derivative of y i.e., f'y=m

Q: Find f. f '(t) = 4 cos(t) + sec2(t), -r/2 < t < t/2, f(T/3) = 4 TC + tan 3 +4 -3/3 3 TC f(t) = 4 sin…

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Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

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Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: 8.. If L' { f(p)} = F (t) then L1 {f( ap) } is : a) aF(at) b) F (t/a) c) F(at) d) (1/a)F (t/a)

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Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: Let f(x) = x² sin(1/x) for x = 0 and f(0) = 0. (a) Use the definition to show f is differentiable at…

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: 2r + 9(x)+ sin(rx). (2) Let f(x) = g where g is a differentiable function such that )-1-4 ) - d(1) =…

A: Given: f(x)=g(2x+12g(x)+sin(πx))g(14)=1−22=1−12g'(14)=2π2=π2g'(1)=3f'(14)=?

Q: 1. f(r +h)-f(r) Using f'(r) = lim %3D Find the derivative of f(r) = V3x- 4. %3D

A: To find the derivative of f(x)

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: suppose f(x) and f'(x) have the following values. I -1 0 1 2 f(x) 6 -9 2 -3 f'(z) -1 5 -6 -2 et h(z)…

A: Given query is to find value of the Indicated derivative using the table.

Q: Let f(x) = tan (cos(2æ)) f'(x) = Preview

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Q: ex+1 b) Find f'(x) of f (x) = x2+3 %3D c) For y = xk+1, where k is a constant. Find y'".

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Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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Q: Let f(x) = x?sin (-) for x + 0 and f(0) = 0. c) Show that f'is not continuous at x = 0.

A: Given function  f(x)=x2 sin1x      for x≠00                  for x=0 we have to show that f' is not…

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

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Q: Find y as a function of x if y" + 16y' = 0, y(0) = 0, y'(0) = 4, y'(0) = -32. y(x) =

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Q: Find the derivative (dy/dx) of the following functions: I) y = (sin x + cos x) sec x

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

A: Let f be a differentiable on an open interval I i.e. (a,b), Suppose that f'(x)=0 for every x in…

Q: Vリ What is F'(;) 4 ? 16 π 4 π ミ|N

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