Q3: A. By power series, prove that: d Cosx = -sinx dx B. Find the value of x for which Inx + (Inx)² + (lnx)3 + (lnx)* + -.. = 9

Q: The volume of water in a right circular cone of base radius 6 inches and height 18 inches decreases…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: The given integral,     ∫13xx2+9dx, n=5

Q: Solve 4 cos (x) 13 cos(x) – 12 = 0 for all solutions 0 < x < 27 I = 138.6 Give your answers accurate…

A: Let's find.

Q: Find the work done by F over the curve in the direction of increasing t. F = xe 7x2 i + e 7y j + e…

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Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

A: We have to sketch graph of parabola then identify the vertex, focus, directrix, endpoints of the…

Q: Use the linear approximation of the following(Answers are to be expressed in 4 decimal places) f(x)…

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Q: Question Write the following using sigma notation and then evaluate. The sum of the terms 2k-1 + 4…

A: We have to write using Sigma notation and then evaluate

Q: 4. f(t) = teatcosbt 5. f(t) = 7t + 6et – 2e-t -10

A: 4) f(t)=teatcosbt 5) f(t)=7t+6et-2e-t-10.

Q: 18

A: We will solve the problem using method of substitution.

Q: Find the arc length of y = +(x + 2)³ + (x + 2)-1 for 1 < x < 2. (Give your answer to three decimal…

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Q: 1) (3,4), (4,3) Ans. Independent

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Q: Question Given f(x) below, find f' (x). f(x) = %3D cos (x) Provide your answer below: f'(x) =D…

A: Given query is to find the derivative.

Q: Find the equation of the fangent line to the graph of the function f (z) sin (3,/7) at the point…

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Q: (x- 2), (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A: This question is related to Straight lines, we will solve it using given information.

Q: 1 dx (x + 1)2 -2

A: We have to determine whether  ∫-2o{1/(x+1)2 }dx  is convergent or divergent.  Let I =  ∫-2o{1/(x+1)2…

Q: Use "w) = d 1 1 to find the derivative of the inverse at the indicated point. dx d 1 Let f(x) = 2x+…

A: Given : f(x) = 2x + ex cos x

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Q: Question Ris the region bounded by the functions f(x) = 6. and g(x) = 2x - 6. Find the area of the…

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Q: 1. Use deductive reasoning to show that the following procedure produces a number that is equal to…

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Q: Determine an equation of the inverse of the function y = 5x + 2. A. y= x+ 2 X- 2 С. %3D B. y= 5x- 2…

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Q: Find for each following dx (i) y = In x', (ii) y=Vx' +3x,

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Q: Use the transformation u = 3x + 2y, v =x+ 3y to evaluate the given integral for the region R bounded…

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Q: Find * L(e2t t²)

A: We will use first shifting Theorem to solve this question.

Q: By considering different paths of approach, show that the function below has no limit as…

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Q: Question 3 (- whether it is convergent or divergent (show all ) Test the following series your…

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Q: 3. Find the area of the loop of the curve y? = 4x'(1-x)

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Q: In Exercises 3, 5, 7, 9, 11, and 13, graph AFGH with vertices F image after the similarity…

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Q: e the substitution x = 3 sin t to evaluate the integral ſ V9 – x² dx. ote: Use C for an arbitrary…

A: Topic:- integration

Q: 30..answer no 7 do like example 6 solution

A: We will find the rate of change of surface area.

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. 7x dx…

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Q: 2) Consider the function g defined by (7x/y)+ glx, y) • COS log3 (x-y) la) determine дудх

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Q: 16. lim (2 – 3x) = –4 %3D

A: Concept: Epsilon-Delta Definition for Limits: The Epsilon-Delta Definition for Limits, also known as…

Q: Find the curve's unit tangent vector. T(t) = Di+Dj+Ok

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Q: Consider the following integral. eu du (5 - e")2 Find a substitution to rewrite the integrand as -…

A: Topic = Integration

Q: I. Find the Laplace Transform of the given function using the definition of Laplace Transform a.…

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Q: 32 RELATED RATES TUTORIAL 32 d0 when the angle is TC radian ? top of the ladder and the wall…

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Q: Suppose f(x) = x° + 3, xE[- 1, 2]. (a) Find the slope of the secant line connecting the points (x,…

A: Given : f(x) = x3 + 3 ,x∈[-1,2] (a) Find the slope of the secant line connecting the points (x,y) =…

Q: Question Suppose the following sums are given. 120 120 2 a; = -2 2 a; = -19 i=1 i=44 Compute 43…

A: We have to find sum

Q: 4. Find the moving trihedral of the curve f(t) at the indicated value: †(t) = cos? t î + sin² t ĵ…

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Q: ) find w=utiv if the function in telm of 2 is (Z-323) (2Z+2) frz) =

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Q: 6. Find the intersection of the line I and the plane t. 1:7 = (4,–1,4)+t(5,–2,3) T: 2x+5y+z+2=0

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Q: b) Is the series is convergent n2 + Vn2 + 33n + 10 n=1 or divergent? justify your answers.

A: Limit Comparison Test : Suppose we have two positive term series ∑ an and ∑bn .And suppose that  L=…

Q: Let D be the solid unit cube: 0 < x < 1, 0 < y < 1, 0 < :< 1. Let S be the closed surface boundary…

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Q: Given that L"(+4²+9)) = 8in(Bt) – sin(Dt) t of Match the following values. 10 is the value of…

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Q: Evaluate the following integrals Li l2l e(1+x²) dx i.

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Q: sec? r, Find the volume of the solid obtained by rotating the region bounded by y = T = 0, x = and y…

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Q: Determine if the function is odd, even or neither * x2-1 x²+1

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Q: Given f(x) = (2x -3) (x+1). Determine (if any)

A: Differentiation

Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms ofr.

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Q: Find a point on the curve x + y = 25xy other than the origin at which the tangent line is…

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