Find the sum of the convergent series. 6 Σ 9n2 + 3n – 2 n = 1

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Q: 2. 4. 6. . (2n) n! n = 1 Identify a, 2n! n! 2.4 6 (2n) n! (2n)! n! (2n)! 2 4· 6 • . . · . (2n)…

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Q: (b) А — В (с) 2A (d) 2A – 5B

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Q: Consider the two series: 6n (a) 5n + 39 n=1 1 (b) n2 In n n=1 Which of the following statements is…

A: Given

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A: We know that integration power rule is - Integration of xn is xn+1/n+1+ C  Here C is integration…

Q: 1. Lets say Q(x) = 5x + 2 P(x) = 3x2 - 5x +1 Find (a) Q (-3) (b) P(5) (c) 5P(x) – 20(x) (d)…

A: Let's find.

Q: x + 4 dx x² + 2x + 5

A: ∫x+4x2+2x+5dxx+1 is a scalable factor of x2+2x+5, so divide x+4 by x+1=∫x+1x2+2x+5dx+∫3x2+2x+5dx

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 7 sin(x). If f(0) = 2 and f'(0)…

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Q: 2. Find the area bounded by the curve y = x³ – 3x2 from x = 0 to x = 2. -

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Q: Evaluate the integral (Trigonometric Substitution) 4 x*dx (x² + 1)²

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Q: Evaluate the integral sec² x tan? x + sec x (sec² x + 1) dx 2 sec x tan x (sec2 x + 1)

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Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: 2. Write the given (total) area as an integral. (vde a. The area above the x- axis and below y = 4–…

A: Here we have to find the area.

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Q: 4e-1dx = 7.96 × 10° O True O False

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Q: Q.3. Use the method of Laplace Transform to solve the initial value probl y"+y +y 3 sin(2t), y(0) =…

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Q: Problem 2: Given a function 4x -1 f(x) = 2x +1 Use tabular method to determine if the limit of a…

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Q: Find the center of mass for the following masses along the x-axis (distances are in cm): 42g at…

A: Center of mass = sumation of mi xi / summation of mi

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Q: y=f(x) A1 АЗ 15 A2 7 A4 10 (figure is NOT to scale) Evaluate the integral below by interpreting it…

A: To evaluate the integral below by interpreting it in terms of areas in the figure.The areas of the…

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Q: - 47 f(x)dx = 12 - 51 | and - 47 |. 9(2)da = 20 – 51 and - 47 - I h(x)dx = 32 - 51 what does the…

A: We can solve the integral as below.

Q: 10* dx (10*+1)5

A: We can solve the integration as below.

Q: 4. 2 cos(2x – y) dx – cos(2x – y)dy = 0 - %3D

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Q: sin x dx (2 + 3 cos x)2

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Q: An ellipse has centre (0,0) and vertices on the y-axis. The minor axis has length 10 and the major…

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Q: Use the product rule to find the derivative of (- 72° – 4x10) (5e² + 4) | Use e^x for e". You do not…

A: This question is related to differentiation, We will solve it using given information.

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1)

A: The given integral is:∫-2x+4x2+1x-1dxWe need to evaluate the above integral.

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A: Volume

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Q: ind The Area Using Integration and Make a sketch of the grap

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Q: What is the equation of the line that contains the vertices of the hyperbola (z+ 4)2 (y+2)² = -1? 16…

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Q: 9. Find the volume of the parallelepiped defined by the vectors. [8, – 3,4] [- 2,9, 1] w = [0, – 4,…

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Q: de 1+sin e+ cose CO

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Q: The graph of f is given. Use the graph to compute the quantities asked for. (If an answer does not…

A: Above asked questions are given below.

Q: xªdx J (x2 + 9)2

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Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

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Q: 4. Find the integral of your answer in problems 2a and 2b. CO

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Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: To find the equation of curve

Q: 19 at are the equations of the asymptotes for the function y = tan 27x where 0 < x < 2 х %3D 0.25,…

A: Given query is to find the equation of asymptots for the function.

Q: S(e3t + e-3t)2 dt

A: To evaluate the value of given integral.

Q: ider the function f(x) = 3 – 72² on the interval [- 6, 7]. Find the average or mean slope of th cion…

A: We wil use the mean value theorem.

Q: Let f(x)=5x/2 - ex . Find the value of x for which f''(x) equals zero.  A. 0 B. 5e C. ln5 D. e5…

A: Solve for x by differentiate f(x) with respect to x.

Q: Directions: Prove the following statements. 1. If f(x) = (x² – 1)3 then f'(x) = 6x3 – 12x + 6x.

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Q: Find the arc length of the graph of r(t) = eviti + e¯V#tj+ 2tk, 0 <ts v2 In 5 NOTE: Enter the ezact…

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Q: (a) On what intervals is f increasing? (Enter your answer using interval notation.) On what…

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Q: (1) Which is the correct formula for finding the derivative of the product of two functions? O (fg)'…

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