Evaluate sin³ x cos²x dx.

Q: What is the slope of the tangent line to the curve y=−2x^2+8x+2 at the point where x=5?

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Q: Find the equation of the tangent line to the graph of the functic f(x) = 3x² - 4x +5 at the point…

A: Find out the equation of tangent line.

Q: Evaluate the function at the given value of the independent variable. Simplify the results. f(x) =…

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Q: Evaluate the following indefinite integral Show work: √ (3x² - 4x + F(x) = 1x + 5)² (3x − 2) dr. B

A: To evaluate the integral

Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: Two fire-lookout stations are 14 miles apart, with station B directly east of stat notation is N35°F…

A: Let the position of fire be at C. Given, Distance between two fire lookout stations AB= 14 miles…

Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: Express the limit lim n→∞ a = n b = i=1 Provide a, b and f(x) in the expression (6 cos² (2πx)+5) Ax;…

A: To find value of a, b and f(x).

Q: Consider the two-dimensional vectors a and b. a = (3,-1), b = (-5, 0). (a) Find the measure of the…

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Q: 25. The vector field F(x, y, z) = (2xy + tan x)i + (x²-√y² - 1)j is conservative. a) True b) False

A: To determine whether the following statement is True or False.The vector field F→x, y, z=2xy+tan…

Q: Set-up the definite integral that will give the measure of surface area of the solid generated 1 by…

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Q: Which of the following equations describes the nth term for the sequence O (3) -1(9)*** 4 1 1 1…

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Q: Suppose cot(theta)=-2, t in the second quadrant. Find cos(theta)

A: topic:- trigonometry ratios

Q: 7. Solve for cot NI 2 if cos(20) = |L0 5 and P(0) E QIV.

A: Given: cos2θ=-45 To find: cotθ2

Q: 5. Using f(x)=xln√x + 2x; Do each of the following: Find f(x) and f(x) a. b. Find critical values…

A: The given function is fx=x lnx+2x we have to find f'x and f''x use the derivative formulas,…

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: 2x log 2x dr 1 (x²+6x+5)3/2 dr

A: As we know that; The Power Rule: ∫xndx=xn+1n+1+C   1). The given integral is: I=∫2xlog2xdx Apply the…

Q: I. Find the solution set of the following. 1. 2e²3e + 1 = 0

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Q: For all x ER, it is known that 1. Find the value of f(2022) (0). +∞o 2. Find the exact value of f(x)…

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Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: at f'(2) = 6 and f'(6) = -2. Which of the following i there is a local minimum at x = 4 he function…

A: Topic:- calculus        Critical value:-  Where f'(x) = 0  And maximum minimum occurs called…

Q: = 5. Prove the identity: cot(A + B) cot(A − B) = cot² B tan² A tan² A cot² B-1

A: To prove cotA+BcotA-B=cot2B-tan2Atan2Acot2B-1

Q: 2. S (4x+5) x²+4x+20 dx

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Q: Evaluate the following limit: lim ²-25 2-5 2-5 O Does not exist. O 0 O-10 undefined

A: This question can be solved using the concept of limits.

Q: Find the volume V of the solid of revolution that results when the region under the graph of f(x) =…

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Q: Set up an iterated triple integral equal to 3 3-x² x²+y² 3 2-√4-x²-y² using: Spherical coordinates…

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Q: Evaluate the definite integral: 0.8 4ze-2%dz = -0.2

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Q: Let y(x)=−3/x^2. Find y′(−3). Enter the exact value, i.e., no decimals

A: given  y(x)=-3x2=-3x-2

Q: 5. Use the divergence theorem to evaluate the surface integral ff, F. ds, where S is the sphere x² +…

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Q: . For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

A: The solution is given below

Q: Which of the following grapins represents (x2}? + y + 47 = 25? - d 7 - 4 41 층 4 $ 4 2 .

A: The given equation is: x-22+y+42=25 First, draw the graph of the given equation.

Q: Find the volume of the solid with the given base and cross sections. The base is the circle x² + y²…

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Q: Find the volume of the solid generated by revolving about the y axis the region under the curve…

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Q: Given that answer = [*f(x) dx = 45 13 > [². what is f(v)dv?

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Q: 5. S (2x²-3x+10)dx (x²+4)²

A: I have stated the used formulas in the solution

Q: ₁+∞ n(3x + 2)n n³ + 4 Given the power series Prove that the series is absolutely convergent when x =…

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Q: Use partial fractions to find the power series of the function. 130 (x2 + 1)(x2 − 25) ∞ n = 0

A: Use partial fraction to find the power series of the function

Q: I. Find the solution set of the following. 4. cos ¹(2x) + sin¯ √√1 - 4x² = π

A: To find the solution set  of the following.cos-12x+sin-11-4x2=π

Q: Given f''(x) = - 36 sin(6x) and f'(0) = 6 and f(0) = 0. Find f(1) = [

A: Given the function f''x=-36 sin6x and f'0=6 and f0=0 use the integration formulas,…

Q: 1. √ 2x log 2x dx

A: The objective of the question is evaluate the indefinite integral. Note -  As per our guidelines we…

Q: Use the Ratio Test to determine whether the series is convergent or divergent Identify an 00 Σ (1)"…

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Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

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Q: 2 s x² dx x2-4

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Q: The total cost of producing x newspapers is given by the function C(z) = 20x-x². Find the marginal…

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: X √x dx 5-х

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Q: 12. Find the area of the part of the surface z = xy that lies within the cylinder x² + y² = 1. a) I…

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Q: 8 1 4-x² 4 x¹ +4.x² dx

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Q: Use integration by parts to find the antiderivative of f(x) = ln(x).

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Q: Find the total surface area and volume of the solid object shown to the right. Use the key for s The…

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