Use Linear Approximation to estimate Af = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation. Give your answer to five decimal places.) Af =

Q: Find derivative of the function f(z) = (sin¬' (2z – 1))² with respect to z.

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Q: Evaluate the derivative of the function. - 1 f(x) = sin(5x) %3D f'(x) =|

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Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: Use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 3. Find the derivative of g(z) = V9- using the definition of derivative.

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Q: Use the Power Rule to compute the derivative.

A: The power rule of derivative is given by: ddxxn=nxn-1

Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 9 sin(x). If f(0) = 4 and f'(0)…

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Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: Use the Power Rule to compute the derivative: d. X. dx x=-1

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: b) f(x) = xe

A: If f(x) is a function of x and the second derivative of f(x) exist at any stationary point x0.1.If…

Q: Use the definition of a derivative to find f'(0) where: x² sin () lo x + 0 f(x) If the derivative…

A: follow next step

Q: Find the derivative of the function. f(x) = sin-(4x) f'(x) = %3D

A: The given function is: f(x)=sin-1(4x) To find f'(x) here.

Q: The derivative of f(x) = cos-(2x) is:

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Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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Q: use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of f(h(x))?  What is the slope of the tan line at x=0.  f'(x)=(3x^2)+3 h(x)=2x+1

A: Given function

Q: Find the second derivative of the function. f(x) = sin(2x?) %3D f "(x) = 16x sin 2x) + 4 cos 22)

A: Given f(x)=sin(2x2) Formula: Derivative of sinx  = cosx Derivative of cosx = -sinx

Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 4 sin(x). If f(0) = 4 and f'(0) =…

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Q: · f(x) = sin(In r²) %3D

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Q: Consider the function f (x) whose second derivative is f"(x) = 10x + 8 sin(x). If f (0) = 2 and…

A: Given function is

Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Determine the points in the interval [0, 2π) at which the graph of the function f(x) = √2x + 2…

A: We find point of tangent on given curve.

Q: g(x)%3Dx sin(2*)

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Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…

A: Given: (1) f(x) = sin x / x  at x = π/6  (2).  f(x) = ex sinx at  x= 0 (3).  f(x) =  cos x / ex   at…

Q: Compute the derivative f'(x)given sin x 1 dt 1- 12 f(x) = cos x

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Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

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Q: Find the derivative of the function ffor n = 1, 2, 3, and 4. sin x fx) = - (X), I n =4 Use the…

A: Solve for the derivative

Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 3 sin(x). If f(0) = 3 and f'(0)…

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Q: Find the derivative and simplify A. f(x) = 2 sin−1(4x + 5) B. f(x) = x3tan−1(x2)

A: Given:- A.   f(x) = 2 sin-1 (4x + 5)   B.    f(x) = x3 tan-1 (x2)  To find :- Derivative of given…

Q: Find the local linear approximation of f(x) = tan¯(x – 4) at xo = 5, where Ax = x – 5. Enter the…

A: Given: fx=tan-1x-4

Q: Consider the function f(x) whose second derivative is f''(x) = 10x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Given, f''(x)=10x+8sinx(x) After integrating the above equation,…

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Consider the function f(x) whose second derivative is f" (x) = 9x + 3 sin(x). If f(0) = 3 and f' (0)…

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Q: f(t) = sin²(e in²s) %3D

A: Given : ft = sin2esin2t

Q: Use the definition of a derivative to find f' (0) where: x² sin() x + 0 f(x) = x = 0 If the…

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Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

A: Given function is f"(x) = 9x + 10sin(x)

Q: Use Part I of the Fundamental Theorem of Calculus to find the derivative of the function. 8(x) = f…

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Q: a) f sin(x) cos(x) dx,

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Q: The derivative of the function () y = In is: tan x,

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: