Find the area between the curves f(x): 3x² 12 (in dark blue) and g(x) = -x² + 4 (in dark red) over the interval [−3, 3]

Q: Use partial fractions to find the power series of the function: 52+74 (x − 9) (x + 8)

A: f(x)=5x+74(x−9)(x+8)5x+74(x−9)(x+8)=Ax−9+Bx+8

Q: Evaluate the following. √6 / (x - 5y + 2) ds S S: z = 11 - 6x + 8y, 0 ≤ x ≤ 5,0 ≤ y ≤ 1

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Q: Express the limit as an integral. 4 lim (7(x)² - 2(x, ) ³) 4x over [0, 4] n→ ∞o Σ i = 1 dx

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Q: Find the Maclaurin series of x5 e7x

A: f(x)=x5e7xWe know that the Power series of ex is given asex=∑n=0∞xnn!

Q: A square-shaped sheet of ice is growing as time passes. If the sheet of ice is always in the shape…

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Q: A swimming pool has a depth of 5 ft at the shallow end and 10 ft at the deep end. The bottom of the…

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Q: The surface whose equation in cylindrical coordinates is r = 5 is... a cylinder a cone half of a…

A: The objective of the question is to identify the type of surface represented by the equation r = 5…

Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by fat x = a. 1 f(x) = -— , a=3 X…

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Q: Use the First Derivative Test to find the location of all local extrema for the function given…

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Q: 1. Use Newton's Method to find the third approximation - x3, for the root of f(x) = x³ - x²-1=0.…

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Q: Find the work done by the force F = -2yi + 4xj along one loop of the curve r direction). = sin 80…

A: The given force  along one loop of the curve

Q: Why is multiplication and division of rational expressions easier to calculate than addition and…

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Q: 2. Determine the value of the discriminant for the quadratic equation y = 1.4x² - 6x +5 and use that…

A: we are given the quadratic equation and we need to find its discriminant.

Q: Find the equation of the orthogonal of the set of the curves and solve the differential equation:…

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Q: Evaluate the integral by interpreting it in terms areas. L(7x-14) de Part 1 of 3 We are concerned…

A: The given integral is The function

Q: A) lim x²-x+1 5/3 x+2 3

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

Q: √√5 3

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Q: PRACTICE vested at a rate of r = 6% compounded annually, monthly, daily, and continuously. (Round…

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Q: Multiply both sides by (x² + 1)² and combine like terms. x² + 6x + 1 = (Ax + B)(x² + 1) + Cx + D =…

A: The given equation

Q: F(x, y, z) = (2xz + y²) i + 2xy j + (x² + 6z²) k C: x = t²2, y = t + 2, z = 2t - 1, 0≤t≤1 (a) Find a…

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Q: #2.) S sec secx tanx sinx (secx) dx

A: we need to find out the integration.

Q: Evaluate the Taylor series expansion of degree four for the given function at the specified point.…

A: f(x)=ex/4,a=4A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 43 km/h…

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Q: I’m not really sure how to solve i’ve tried several times.

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(t)√1 sin(t)√1 +…

A: To evaluate the following indefinite integral.

Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

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Q: 9. The radius of a large balloon is increasing at a rate of 2 inches per second. How fast, in cubic…

A: Let r be the radius of the balloon and V be the volume of the balloon That is we are to find the…

Q: Given the values of the derivative f '(x) in the table and that f(0) = 195, estimate the values…

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Q: Graph this system of equations to find the area between the curve: 2y=4sqrtx y=3 2y+4x=8

A: To draw the graph of the following system of equations to find thearea between the curve.

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: The given function is The linear approximation at  is The quadratic approximation at  is

Q: Solve the rational equation below, please upload a picture of your work. 243 +2³6 - 27 2-32-18

A: To solve the following rational equation.

Q: Using the appropriate substitutions sin sin 20 = 2 sin 0 cos , evaluate the integral. 16 cose Ꮎ ᏧᎾ…

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Q: Congratulations! your answer is correct (and saved). Check Answer/Save Step-By-Step Example Find…

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Q: Let G be a function whose derivative is shown below. Assume the domains of G and G'are 0 ≤ x ≤ 12. 8…

A: We have given a graph of G'(x) in the interval . We have to find the value of G( 6) and coordinates…

Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

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Q: Set up the integral that computes the volume of the region W in R³ bounded by the surfaces z = 0, x…

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Q: Compute the area of the surface obtained by rotating the curve y = 1+ 2x², 0 ≤ x ≤1

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Q: Use the Ratio Test to determine whether onvergent conditionally, or divergent. n=1 (−77)” n! is…

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Q: Use the half-angle formula cos² 0 = 16 V cos² cos2 Ꮎ ᏧᎾ 6 = 1/²/(1+ = 1/6/6/²2 ( ¹ + [ 1 8 ([ 1) + C…

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Q: Find The derivatives: @-ª [secx - 5c0sx] d dx @y=3x²³ + sin x +5 cos x m yle) (sinx) y= и @y= 5 2 y=…

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Solve the rational equation below, please upload a picture of your work. 14 2²2-22

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Q: 10 [²0: 9x - 1 x²(x + 1) dx = - [ ²010 dx - [10 / / + dx - 1²0 x 140 1 dx +

A: I=∫1109x−1x2(x+1)

Q: Compute JJJ³ 32² dV, where W is the solid sphere x² + y²+z² ≤4.

A: Computewhere  is the solid shpere

Q: Suppose f is differentiable and f' is increasing on an interval (a, b) (that is, f is concave-up…

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Q: In the following exercise, given that 1 1-x = ∞ Σa x" for x < 1, n=0 use term-by-term…

A: Power series.

Q: Given the graphs of polar equations: r = 1 and r = - 2 sin 0, (a) Set up the integral that gives the…

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Q: a) The rectangles in the graph below illustrate a The value of this Riemann sum is left endpoint…

A: given function f(x)=

Q: Evaluate the integral by interpreting it in terms of areas. 4 [3₁ |x| dx

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Q: The graph of g is given below. 6 5 -6 -5 3 Log(x) dx -6 4 -6 + Use the graph to evaluate each…

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Q: Find the value of k that makes the antidifferentation formula true 1 - dx 3+ 7x k Inl3+ 7xl +C

A: To find the value of  that makes the antidifferentiation formula true.