Find the derivative of the function. g(0) = (cos(70))4 g'(0) = || X

Q: Solve the following non-homogeneous differential equations: 1) x"(t) + x(t) = 2 cost

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Q: Evaluate the following limit. lim 8+←8 15 ln x X = Note: Input DNE, infinity, and -infinity for does…

A: Given,

Q: Find the vertex form of the function. Then find each of the following (A) Intercepts (B) Vertex (C)…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: You will integrate the following rational function: -5*²+*+13 da (*-1)² (+2) To do this, start by…

A: To evaluate the integral

Q: Suppose f (x, y) =x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Consider the function f(x) : = m2 – 52+4 x + 2 a. Find the first derivative. f'(x) = b. List any…

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: Find the exact average value of f(x) = rlnr on the interval [1, e] (do not approximate).

A: The average value of function f(x) over the interval  is The given function is

Q: You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 6…

A: The angle of elevation is denotes by Horizontal distance denotes by x Verical distance denotes by y…

Q: 18. Find dy/dx by implicit differentiation.

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Q: 3 11 (1 + ³²) ² lim (1+

A: L=limx→∞(1+3x)x11

Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: y = = = = ₁ y = 0, 1 ≤x≤ 2 al Find exact coordinates of centrod b) sketcn the region bounded by the…

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Q: If y = cos² 3x, then =? dy dx dy dx O dy dx dy dx = 6 cos 3x = = -2 cos 3x -6 sin(3x) cos(3x)

A: Given,

Q: The temperature at a point (x, y) is 7(x, y), measured in degrees Celsius. A bug crawls so that its…

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Q: (b) Isolate дет 11 2x 5 = 1/2gt²2² + vt

A: To isolate  in the following equation.

Q: (2x - y) + (2y - x)y' = 0, y(1) = 3

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Q: Consider the following set of data. 12, 13, 13, 15, 16, 17, 18, 20, 20, 20, 22, 26. Compute the…

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Q: In 1993, the moose population in a park was measured to be 3920. By 1997, the population was…

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Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

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Q: Compute the average rate of change of the function on the given interval. g(x) = x³ x on [4, 5] -

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Q: Profit The profit P (in dollars) made by a cinema from selling & Bags of popc x² 28,000 3,300, 0≤x≤…

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Q: Let f(x) = Then f'(x) = π The equation of the tangent line to y = f(x) at a = can be written in the…

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Q: Consider the graph of distances from the origin as a function of time for a car trip. 150 100 50…

A: This all the given problem by using the concept  slope of tangents at a point.

Q: Evaluate the following integral, S yx² ds where C is given by y x5 for 0<x< 1. =

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Q: What is the difference between the disk (or washer) method and shell method? Please provide your…

A: The disk (or washer) method and the shell method are two different techniques in calculus for…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Consider the sequence

Q: Consider the function f(x) = = 8x² x-6

A: f(x)=8x2x−6

Q: Determine whether the statement is true or false. If f and g are differentiable, then [f(g(x))] =…

A: Given statement (d/dx)[f(g(x)] = f'(g(x)). g'(x)

Q: y = (cos 7x)x

A: y=(cos⁡7x)x

Q: Find the volume of a solid obtained by rotating the region bounded by the curve y sin x and the line…

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Q: 2. Differentiate the following functions. a. b. Differentiate the following function. f(x) = 775…

A: (a) f(x)=7π6

Q: Consider the following situation. A company purchased computers for each employee and two all-in-…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Find the derivative of the trigonometric function. y = sin((πx)8)

A: y=sin⁡((πx)8)

Q: . D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x…

A: The given function is

Q: Suppose that an airplane flies along the path r₁(t) = (2t, 2t², 10e-t) and a skydiver takes the path…

A: Given that the an airplane flies along the path  and skydiver takes the path  for

Q: Find all critical numbers c of f(t) = 3t²/³ +t5/³.

A: f(t)=3t2/3+t5/3

Q: Use upper and lower sums to approximate the area of the region using the given number of…

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Q: Given that (fog)(x)=x-8, which are correct rules for f(x) and g(x) that result in this composite…

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Q: Exponential Growth: a. The table below represents an exponential function. Find the missing values.…

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Q: 2. Set up iterated integrals for both orders of integration. Then evaluate the double integral using…

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Q: Solve the given boundary-value problem. y-10y+25y=0, y(0)=1 y(1)=0

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Q: Determine if the series diverges. If it does diverge, type a upper case D as your answer, and if the…

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Q: 1. xaxy - 4y = x6 ex dy dx

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

Q: Differentiate the following function to review unit two. a. b. C. d. 11 11 y = ²+1 4 - 3t² + 2 F(x)…

A: y=t2+1t4−3t2+2Take derivative.y′=ddt(t2+1t4−3t2+2)Use the quotient rule for the derivative:…

Q: Find the marginal cost function. C(x) = 190 +5.7x-0.07x² c'(x) =

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Q: Find the surface area of the part of the plane 4x+3y−z=2 that lies above the box 2≤x≤5,   2≤y≤6…

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Q: 1. Solve dy_3-x-y x + y €1 dx 11

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