Find the indefinite integral and check your result by differentiation. (Use C for the constant of integration.) 1- dt

Q: Let ƒ(x) = x³ + 3x² − 9x + 22. (a) Use the definition of a derivative or the derivative rules to…

A: The given function fx=x3+3x2-9x+22 use the derivative formulas, ddxxn=nxn-1ddxax=addxa=0 where, a be…

Q: (4) (d) 2-7 dx 4x-2 x²-1 (4) (e) S 7x (4x²+5)3 dx

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Q: EQUATIONS 5y" - (y) = y³ sin æ 4 x yy" + 2x = tan x ºr + (5) - w = 4et St2 88 SM - (SM) dy³ xt' +…

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Find the average value of the given function from x=0 to x=1. Sketch graph of the function, roughly…

A: Average value of a function y=f(x)  from x=a to x=b is given by Aavg=1b-a∫x=ax=bf(x)dxsee below the…

Q: The volume of a right circular cone of radius x and height y is given by V = volume of the cone is…

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Q: Find F as a function of x and evaluate it at x = 0, x = 7/3, and x = 7T/2. F(x) = F(x) = F(0) = (7)…

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Q: 23 -x³ Submit Question Find all local extreme values of f(x) The FIRST local extreme value, moving…

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Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: Sam makes $25.00 per hour. He gets paid time and a half for overtime. He gets paid every week. He…

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Q: What is the equation of the tangent line to y=−2x^3−x^2+4x+3 at x=3? Write the tangent line in…

A: We have to find the equation of tangent line.

Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: Solve the following system of equations using the Gauss elimination method 4x - 3y + 2z = -16 -3x -…

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Q: Consider the function f(x) = 4 − 2x² on the interval [ – 2, 3]. Find the average or mean slope of…

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Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

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Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

Q: = Approximate the area under the curve y = x² from x with 6 subdivisions. 3 to 6 using a Right…

A: We have to approximate the area under the curve using Right Endpoint Approximation.

Q: Given the function f(x)= |x-1|: (a) explain why f(x)= |x-1| does not have an inverse function over…

A: Given fx=x-1

Q: Which if the following is a power series representation of the function f(x) a. Σ(-x - xn+¹) n=0 Ob.…

A: We have to find the power series representation for given function.

Q: Question 6 Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0…

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Q: kmarks Window Help 0 -7- The graph of f(x) is given below. Which of the three conditions for…

A: Given qiestion:- The graph of the f(x) is given below. Which of the three conditions for continuity…

Q: For an object in an elliptical orbit around the moon, the points in the orbit that are closest to…

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Q: 1. x²yy' = ey =

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Q: im not really understanding because its typed

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Q: Consider the function f(x) = 4x + 4x7 4x³ 8. An antiderivative of f(x) is F(x) = Ax" + Bxm + Cx² +…

A: The given integral is fx=4x9+4x7-4x3-8 Integration formulas: ∫xndx=xn+1n+1+C∫dx=x+C

Q: 3. State the components of a unit vector that is perpendicular to the vector = (5,2,−1).

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Q: Suppose that f(x, y) = e e-x² - 2y² + x Then the maximum value of f is

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Q: .1 Simphiwe bought meal tickets to use at the school's cafeteria. E requires 2 tickets, and she…

A: Topic:- application of algebra

Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: A y 10+ -10-8 -6-4 -2 8 9 2 2 7 6 8 -10- 2 45 8~9 10 X

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Q: = 5, A2=3, A3=1 and A4=1

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Q: d the equation of the tangent line to the curve y = 5x cos x at the point (7, e equation of this…

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Q: Answer all of the questions below about the function f(x) graphed below when x = 5. 8 8 f -10…

A: Given Graph:-

Q: If f(x) f'(x) = [ 7-x² 3+x² find:

A: Topic = Derivative

Q: f(x) = √x²-2 7+|x6| S if x < 2 if x ≥ 2

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Q: 6) Line y=x between x = 0 and x = 1 is rotating around the x - axis. (It forms a cone). Calculate a)…

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Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: Σa_₁ (-_^_-) n² 'n n+1 Select one: O True O False is convergent.

A: To determine whether the following statement is True or False.∑n=1∞ nn+1n2 is convergent.

Q: f(x) = -2x² + 7 7x 10 - if x ≤ −1 if x > -1

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Q: 12 76 Exercises (if possib 15. y = 5x + 3 17. y = -x - 1 19. y − 5 = 0 0 1 23. 7x - 6y = 30 020…

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Q: y-e-x4cos4x ស

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Q: Find the exact area of the region bounded by 2y = 4√√x, y = 4, and 2y + 2x = 6

A: Here we have to find the area of the region.

Q: x2-x1/3=0 x1/3(x5/3-1)=0 How do I get to the final simplification from the first equation?

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Q: Find all intervals on which f(x) is increasing. f(x) = x³ + 7x² + 15x + 45

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Q: Evaluate the following limits. If needed, enter oo for ∞ and -oo for ∞, and DNE if the limit does…

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Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

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Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation.

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Q: Sketch the region enclosed by y = 5x and y = 6x². Find the area of the region.

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Q: For the function ƒ(x) = x² – 11, find the equation of the tangent line at å = −12.

A: Given function f(x)=x2-11 We have to find the equation of tangent line at x=-12 Derivative of a…

Q: 3 14 f(x) dx where a = 5 - ["² f(x) dx = [ f(x) dx 3 a and b =

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