Write a in the form a = a-T+a,N at the given value of t without finding T and N. )3 (7 e*cos t)i+ (7 e'sin t)j+ (7 e'V5) k, t=0 a(0) = ( )T+ (Type exact answers, using radicals as needed.) N

Q: n Apply the Integral Test to the series E n=1 n²+1

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Q: Find the following for the vectors u = 6i + 3j + /2k and v = - 6i – 3j – /2k. a. v•u, Įv], and Ju|…

A: We will solve the problem on vector dot product and projection.

Q: v(x² – y + x)dx + (x² – 2y) dy = 0 %3D

A: Topic:- solution of differential equation

Q: L Find the point/s of intersection of each of the following figures given below, draw the element…

A: The region is bounded by the curve y=x2+2 from x=0 to x=2

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Q: Fill in the blanks: The derivative of a product of two functions is the first function times the of…

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Q: dy without first solving for y. dx e implicit differentiation to find ² + 3x + xy = 100 the given…

A: Topic:-  application of derivatives

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r=5 sint and 0= 5t = (5 cost) u, +…

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Q: 10. The graph of a function is given below. Determine the intervals on which the function is concave…

A: We know that,

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Q: Write the composed trigonometric function sin (arctan x)sin (arctan x) in terms of x. Explain your…

A: In this question we have to find the function in terms of x.

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Q: For an arithmetic sequence, a17 = 2. If the common difference is 5, find: aj = the sum of the first…

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Q: Use the graph of the function f shown to the right to estimate the indicated function values and…

A: topic- limits

Q: Use algebra and the properties of limits as needed to find the given limit. If the limit does not…

A: We can find the limit of the function. Firstly make factor in numerator and denominator and solve .…

Q: "(x) If t(x) = Vx find ť'(x)" -2x O 2x -1/2x O 1/2x O None of these O o o o

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Phi Ms. Kaye of the Lakwatsera tours offers a group rate of Php 24000 per person for a week in Cebu…

A: Concept: Maximum and minimum value: To find the maximum and minimum value of a function using first…

Q: Find T, N, and k for the space curve, where t>0. r(t) = (5 cos t+ 5t sin t)i + (5 sin t- 5t cos t)j…

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Q: Determine if there are zero, one, or two triangles for the following: m ZA = 48° a = 10 m

A: Given:∠A=48°a=10b=12

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Q: 5. ungles can be formed using the given measurements. The other measurements of the triangle in…

A: Two triangles can be formed by using the given measurements. The other measurements of the triangle…

Q: Geometric Sequence A. Find the indicated terms of the following geometric sequences. 1. 12, 6, 18, .…

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Q: Find the area of the region that is enclosed between y = 11x? – 2³ + x and y = x? + 25x. The area is…

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Q: 6. Two triangles can be formed using the given measurements. The other measurements of the triangle…

A: For other triangle m∠B=180-55.092=124.908°m∠C=180-124.908-41=14.092

Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 5 sint and 0 = 5t = (Du, + ()…

A: Recall:The velocity is given by      v =r' ur +(rθ') uθandThe accerleration is given by     a…

Q: Find the exact length of the curve y=1+6x% for 0<xsl

A: We have to find the exact length of the curve y=1+6x32 for 0≤x≤1.

Q: Write a in the form a = a-T+aNN at the given value of t without finding T and N. 3 (5 e'V5)i+…

A:

Q: Evaluate the integral |- 5x + x3 - 2 x5 dx 3

A: Topic:- integration

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Q: x +729 lim x+9 X-9

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Q: Solve cos (w) - 6 sin(w) for all solutions 0 < w < 27 %3D w = Give your answers accurate to 2…

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Q: Problem 12 Find the following indefinite integrals (a) S(9x² + 8x +3)dr (b) S(x-4 – 9/I)dr (c)…

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

Q: 2. Which of the following is a valid trigonometric substitution? (a) If an integral contains 9- 4r2,…

A: Here, to find the valid trigonometric substitution.

Q: dy without first solving for y. dx Use implicit differentiation to find y? 1 36 36 dy dx At the…

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Q: 11. Write true if the statement is correct and false if the statement is incorrect. Given the…

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Q: 12. Find the profit function for the given marginal profit and initial condition. dP = -40x + 290,…

A: Solve the following

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Q: Using the fundamental theorem of calculus, find the area of the regions bounded by y= 5-x^2 and the…

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Q: Find the limit. lim x--s+ (x + 5)2

A: The given limit,limx→-5+1x+52

Q: For the power series E (х-3)" find the interval of convergence. n=2 n5"

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Q: Use implicit differentiation to find the point in the first quadrant on the ellipse 8x2 + 4y? slope…

A: Question- Use implicit differentiation to find the point in the first quadrant on the ellipse 8x² +…

Q: 9. Find the vertical and horizontal asymptotes of the function. X-8 f(x): х2 — х — 6

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Q: Use implicit differentiation to find the slope of the tangent line to the curve x3 + 9 2y - 10 at…

A: Topic:- application of derivatives

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Q: 1 X• In( coS lim (* - In(cos )) x00

A: Given