Find rº' (2) if 7¹' (t) = (4²t, t² – t).

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A: To find the increasing and decreasing intervals for the following functions.

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A: Given,

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A: Let To determine  as a function of t, then to find the slope of the parametriccurve at .To…

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Q: Evaluate the indefinite integral I si 3 sin³ v cos¹vdv + C

A: To evaluate the following integral.

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Q: Let F(x) = f(g(x)). Find F¹ (2) using the following information f(-1) = -3, f'(-1) = 2, g(-1) = -7,…

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Q: Consider the following limit. lim n→∞ an 'n + 1 = 0 What can you conclude about the convergence or…

A: Ratio test states that for a given series ∑n=1∞ an  , let L = limx→a |an+1an| If L&lt;1, then the…

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Q: Find all horizontal asymptotes of the following function. f(x) = 3(x − 8) (x + 8) (2x − 5) (2x + 5)

A: To find all horizontal asymptotes of the following function.

Q: The functions f and g are differentiable and have the values shown in the table. If A = f + g, then…

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Q: let f(x)= = x4 12 ترجمه + 6 - - 3x² +

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Q: 1) Find the derivative of ye

A: Given,

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Q: ₁²(x² + √x)dx g. 32 h. 1 i. f₁¹(r + 1)²dr x-6/5 dx

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Q: [x³v 3 Evaluate the integral: 16x²dx

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A: The given polar curve is .The objectives are to calculate the points where the tangent lines are…

Q: [s sin x cos x esin²x+dx = A B C D - sin x cos x esin²x+ esin²+ + C 1/2 (sin ²x + 7) + C e -…

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Q: Compare the domains and ranges of the following two functions. Using graphing calculator. a.…

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Q: Differentiate the following and simplify. Show all work, thank you! Part ( a) and (b).

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Q: -5 (-2,9) (-1,-1) 10- -10- (2,-7) The average rate of change from x= -2 to x= 2 is found using the…

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Q: Find the length of the cardioid r= 2-2 cos 0. The length of the cardioid is (Simplify your answer.)

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A: IN the given scenario two pathogen genotypes occur in chickens, and one of them is accidentally…

Q: Find the area closed by one loop of the rose r = 5 sin 30.

A: Area closed by one loop of the rose r=5sin⁡3θr=05sin⁡(3θ)=0sin⁡(3θ)=03θ=0,πθ=0,π3

Q: 3) 11 Show that y + y = 0, given that y = 2 sin x + 3 cosx

A: Given,.We know that,

Q: 4) Decide whether the following sequences converge or diverge and why a) {1, 0, 1, 0, 1,....}

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

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Q: Which of the following are Taylor series representations of f(x) = 1 x3 Check ALL that apply a=2

A: given function

Q: Given f(x) = 4x-9, compare the range for f(x)and y=√f(x). O Range of f(x):{yly ER} Range of…

A: The range of the function is the set of all possible output values.

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Q: what is the correct composition of the product or quotient rule? y= sin(x) cos(z) y = 3x y=-3x…

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Q: e) Evaluate the following limit at infinity and show your work. 3x³-4x a) lim x→∞ x²-2x3 Inoso sin…

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Q: 1. How many possible x-intercepts will the function f(x) = Ax5 + Bxª + Cx²³ + Dx² + Ex+F? a. Minimum…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y₁…

A: The given equations of the curves are:

Q: Sketch the graph of the following functions. State the domain and range. y = 2√√x+3

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Q: The functions f and g have the values shown in the table and are differentiable. If A = f g, then…

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Q: Find the tangent plans do z = 2³² + 3xy + 23² Z 8 at X=2 and g=-1 the where

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Q: Set up the integral that uses the method of cylindrical shells to find the volume of the solid…

A: Given that the region enclosed by  and the y-axis.

Q: Use Pascal's Triangle to expand (5x + y) 4. Express your answer in simplest form.

A: The given expression .The aim is to expand the expression using Pascal's triangle.

Q: If f(x) = 1/2 · cos x, then f'(x) = I A B C D sin a x² -1-x² sin x x² cosx-xsin x x² cos x+xsin a x²

A: As we can see f(x) is product of two functions i.e 1/x and cosx.We use the formula for derivative of…