1. Given x= 2t2+ 1, y= 3t : Find A = J ydx as a function of t by substituting for y and dx their values in terms of t.

Q: 6x Find an equation of the tangent line to the graph of y = 2 X +1 at the origin and at the point (-...

A: Given,          The line is y=6xx2+1 at the origin and at the point -1,-3.To find : Find an equation...

Q: Find k such that the function is a probability density function over the given interval. Then write ...

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Q: Ja 1. Suppose a < b< c, solve: i. (x) - g(x)]dx ii. (x)dx

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Q: Sketch y=(x^2-9)/x+3

A: Sol:- y=(x^2-9)/(x+3)=(x+3)(x-3)/(x+3)=x-3 so y=x-3 put y=0 x-3=0 x=3 (3,0) put x=0 y=0-3=-3 (0,-3) ...

Q: Find dy/dx if x^3y^2+2xy=x^3

A: Solving the problem by finding the dy/dx of the given expression.

Q: 9x sin) C-8. Value of dx equals to sinx2)

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Q: ( a) Σ-1"+1, 2η+2 Vn3 + n2 + n n=1 ,2η n2n (b) en3 n=1

A: Given

Q: Locate the critical points and identify which critical points are stationary points. f(x) = 5x – 160...

A: Given thatfx=5x4-160x2+8Solution : find first derivative and equate equal to zero.fx=5x4-160x2+8f'x=...

Q: Find the differential dy of the given function. y = arctan(x - 2) dy dx

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Q: 2.

A: ∫x2ex dxBy integration by parts

Q: Instruction: Answer the following. Show all your solutions. For items 1 and 2: Given f(x)dx = 4; f(x...

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Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan...

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Q: Find the vector component of v = (4, - 1, 7) along b = (2, 3, -6) and the vector component of v orth...

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Q: Let ex + 9, x 2 d. x = 2 Find the values of c and d that make f(x) continuous at x-2. d= (If the va...

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Q: 1. we have to evaluate the following integrals 4 dy de a.

A: a ∫14∫12 (x/y + y/x)dydx ∫14 [xlny + y2/2x]]12dx ∫14 xln2 + 2/x -1/2x ∫14xln2 +3/2xdx [(x2ln2)/2 + 3...

Q: Consider the points A(3,-3, 3), B(4, -5, 1), C(-2,-4, 1), and D(6,3,-5). (a) Find the volume of the ...

A: Given: A(3,-3,3) ,B(4,-5,1) ,C(-2,-4,1) and D(6,3,-5)

Q: A F(s). s2 + 4 1 B F(s) s? + 2 1 ©F(s) S - 2 DF(s). S + 2 S E F(s) s2 + 4 S - 2 FF(s) = (s - 2)2 + 4...

A: Question-  Find the inverse Laplace Transform of the given function-  f(t) = cos (2t)

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /...

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 3ky + k² = 0 and ...

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line x=...

Q: ability density function over the given interval. Then write the probability density ... (Type an ex...

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Q: Find the solution of the following Differential Equations 2) y"+2y'+y x 4) y"+y=-30sin(4x)

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Q: The rate of change of the population of Calcville can be modeled by the function P'(t) = 13.4e0.04 w...

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Q: A rectangular package to be sent by a postal service can have a maximum combined length and girth (p...

A: Given problem:- A rectangular package to be sent by a postal service can have a maximum combined len...

Q: Evaluate the function y = - for x = 3 to x = 5 in steps of 0.5. Write the complete x+ code

A: % Matlab Code% defining the range for xx = 3:0.5:5;y = (x) ./ (x+(1./x.^2))

Q: Find the vector component of v = (4, 7) along b = (2, 6, –9) and the vector component of v orthogona...

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Q: Evaluate the following limits. 1. lim(1+ Vw)(2–- w² + 3w*) w+1 12 - 1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A:   ---------------------------------------------------------------- x2+y2-6ax=0                     ...

Q: Look for the volume of the solid produced by rotating the region enclosed by about x? - 2kx – 4ky + ...

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line x=...

Q: At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 24 knots and ship...

A: Question- At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 24 knot...

Q: Click the play button and note the values of the angular speed w, and the linear speed v. (i) How do...

A: Given query is to find the correct answer for the relation between angular speed and radius , linear...

Q: 2n + 2 (a) E(-1)"+1. Vn3 + n² + n n=1

A: The given series is: ∑n=1∞(-1)n+12n+2n3+n2+n Now, let  an=(-1)n+1(2n+2)n3+n2+n &amp; bn=nn3=1n32-1=1...

Q: 2. Determine f'(-1) for the function f(æ) = (x" – 2r° + 1)(x³ + æ -- 2). 8 (B) 12 (C) 14 (D) -4 (E) ...

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Q: g(y) = y3 dy y 4 3+ 1 4 6. 8

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Q: 5. For f(x) = 2x + 8 and g(x) = 4 - 2x, determine the domain of f(g(x)) %3D SESEASAN

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Q: The sales, S. of a product have declined in recent years. There were 204 million sold in 1984 and 1....

A: The sales, S, of a product have declined in recent years. There were 204 million sold in 1984 and 1....

Q: Consider the rational function y = - -1 when investigating and analyzing. Match the topic with the a...

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as...

Q: 1.3. Study the existence and uniqueness of the solution of the initial value problem (2y – 4)y/ – (3...

A: Given problem:-     To find:- fy(x, y) 

Q: Use the Second Derivative Test to find all local extrema, If the test applies. Otherwise, use the Fi...

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Q: Q4. Approximate the value of f xv2x² + 1dx using the trapezoidal rule with n = 6. Compare this resul...

A: I am attaching image so that you understand each and every step.

Q: 3. Evalnate. the. fallowing.denble.integrals..by.convecking.bo. Can polar.Caa.r.dinates. ... 2 2 I-x...

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Q: Consider the power series rvn(5– 2x)" 2n + 1 Vn(5 – 2x)* n=1 a. Show that the series is conditionall...

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Q: We model pumping from spherical containers the way we do from other containers, with the axis of int...

A: To find the amount of the work.

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month i...

A: Given query is to find the rate of change of cost.

Q: Evaluate lim f(x+h)-f(x) h-0 where f(x) = 2– 3x². h O -3x -6x O 6x O None of these

A: The given function f(x)=2-3x2

Q: Draw a dependency diagram, and write a chain rule formula for and where w = k(r) and r=h(p.q). Choos...

A: Use chain rule

Q: Daily crude oil production by Pemex, Mexico's national oil company, for 2008-2013 could be approxima...

A: Find the derivative using power law of derivative. 

Q: (*q ۔yi( - ريدو )ود( ل )(

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Q: 4 | a sin(3y+ x²)dydx, 2 a) Sketch the domain of integration on an (x,y)-plane. b) Set up the integr...

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Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (х — 2) %3D 4(у + 2)...

A: Given that the area is bounded by x-22=4y+2 and y=-1.It is required to find volume generated by revo...

Q: 1. Determine if the series cos" () en? n=1 is absolutely convergent, conditionally convergent, or di...

A: Given series ∑n=1∞ cosn1nen2