Differentiate the function. f'(x) = f(x) = In(cos(x))

Q: - Find formulas for dy and Ay if y = x² − 7x + 4. **** dy Ay

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Q: 4. Find the exact and the approximate value of x: 2* = 5*-1. Round answer to three decimal places. N

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Q: Evaluate ∫ ∫ √ (x2+ y2) dA where R is the portion of the annulus 1 ≤ x2 + y2 ≤ 16 with y ≤ 0 using…

A: We have to evaluate the double integral.

Q: e-1 Find the limit limä→0 tan x

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Q: The Second Gate As you move through the first gate, you can see another gate not far in front of…

A: Given: g(x) = x+5x2-25 The function does not exist when their denominator is zero. That is,…

Q: x²-1 Evaluate the limit, if it exists: lim - a. does not exist b. 2 *1 X-1 C. 0 d. 1

A: We are required to evaluate:limx→1x2-1x-1

Q: After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's…

A: Given f( x ) = ( x4 - 2x ) g( x ) = ( x2 + 2x - 62 ) h( x ) = 2x - 13

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 4x²-x³, (1, 3) y =…

A: Solution: f(x)=4x2-x3, (1,3)

Q: Differentiate the function. f'(x) = f(x) = e5

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Q: Find the tangent plane to the equation z = 7e²²-2y at the point (4, 8, 7) 2 II

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Q: (x)) = main of f(g(x)). (Enter your answer using interval notation.) (x)) main of g(f(x)). (Enter…

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Q: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

A: Profit = Revenue - Cost

Q: Find √ √1 + x²dx

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Q: Find the Maclaurin series and find the interval on which the expansion is valid. f(x) = ln (1-x²)

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Q: 1 3 I(t) = ²/³ - 5 ² + 3 2 +86 (0 ≤ t ≤ 10)

A: I(t)=13t3-52t2+86for critical numbers put I'(t)=0d dt(tn)=ntn-1d dt(constant)=0

Q: 2 √x (x + 1) ² dx dx =

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Q: Use graphical addition to sketch the graph of f + g. y y f+g 2 f 2 2 f+g g 4 4 4 6 6 6 8 8 X 2 2 f+g…

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Q: Determine if Rolle's Theorem can be ap- plied to f(x) = x² + 3x - 18 x + 3 on the interval [-6, 3],…

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Q: Using the ratio test to determine the convergence or divergence of the series series. Divergent The…

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Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit. tan ¹ n A.…

A: Given;  A. an=tan-1n/n B. bn=Cosn.

Q: Write an equation of the line containing the given point and parallel to the given line. Express…

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Q: Find an equation of the tangent line to the graph of the given function at the specified point. x²-1…

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Q: a) Find all of the critical points of x2 - x - 1 b) Find all of the critical points of x3 - 3x - 2

A: We have to find the critical points.

Q: 6y' - 2y = xy¹, y (0) = -1

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Q: you have 2 . DU also can you do explain the integration by part showing what you are integrating

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Q: As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you lies an…

A: Here is the solution:

Q: Solve the initial value problem for x as a function of t.. (t²-19t+90) dx dt x(t) = (Type an exact…

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Q: Find the volume of the wedge cut from the first octant by the cylinder z = 12-3y² and the plane…

A: We have to find the volume of cylinder.

Q: he given curve is rotated about the y-axis. Find the area of the resulting surface. y =  1 3x3/2,…

A: Given

Q: Consider the function ƒ(x) = x¹ − 18x² +8, −2 ≤x≤7. This function has an absolute minimum value…

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Q: 3. If z=x²y,x=2t+s, and y=1-st², find dz atl=2

A: As per our guidelines, we are supposed to answer only one question at a time. Since you have posted…

Q: Evaluate the Limits: a) limt->-1(t2+3t+2)/(t2-t-2) b) limx->9 (9x-x2)/(3-x1/2) c) limx->-inf…

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Q: cos x ln(sin x)dx

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Q: 5. Find the explicit solution of the given initial-value problem. dy e-x-ex dx 3+4y a) = y(0)=1 (b)…

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Q: Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (4π, 0)

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Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: Identify the open intervals on which the function y=9x-18 cosx, 0<x<2pi is increasing or decreasing.

A: A function y=f(x) is said to be increasing in an interval a,b if for everyx∈ a,b, dydx=f'(x)&gt;0.…

Q: Consider the following. f(x, y) = 9x y A /2 sin(0) 1/2 ([ 0 r = sin 0 (a) Set up an iterated…

A: Given f(x,y)=9x

Q: After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's…

A: Given that , fx=x6-2x , gx=x2+4x-59 , hx=2x-11 and mx=fx·gx , nx=gxhx

Q: Consider the function f(x) = 2x³ - 5x on the closed interval [-4, -2]. Find the exact value of the…

A: We have to find the slope and value of c.

Q: Suppose f(x,y)=xy(1−10x−4y). f(x,y) has 4 critical points. List them in increasing lexographic…

A: We can solve the given problem by using the second derivative test.

Q: 3. Use the limit definition of the derivative to find f'(x) for f(x) = 7x² + x.

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Q: 4 Function f is defined by f(x)= √√x+1, -1<x<1 x-1, otherwise (a) Find lim f(x), lim f(x), lim f(x)…

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Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

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Q: Find the linearization of the following function, at theta = pi/4  f(theta) = sin(theta) cos(theta)

A: The given function fθ=sinθ cosθ. We have to find the linearization of the function at θ=π4.

Q: Let f(x) = 7x sin(x) cos(x). Evaluate 3TT f'(x) at x = 3³77₁ ƒ' (³)

A: f(x)=7xsinxcosxd dx(sinx)=cosxd dx(cosx)=-sinxd dx(a.b)=adbdx+bdadx

Q: Find a plane containing the point (-5,6,5) and the line Calculator Check Answer x (t) y(t) z(t) = =…

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Q: 1 e) lim (-—-—-₂--²-4) x-3x-2

A: M=limx→3(1x-2-4x2-4)

Q: The graph of y = f(x) has ƒ(5) = -2, f'(5) = 2, and f'(5): = -1. Which of the = −1 following might…

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Q: Compute [5t³ - 8t + 1] d dt

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