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Q: Save your solution for this problem to answer the other problem connected to this. Consider the curv...

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Q: Suppose that 5 J of work is needed to stretch a spring from its natural length of 24 cm to a length ...

A: NOTE: Refresh your page if you can't see any equations. . Natural Length=24 cm=0.24 m Extended Lengt...

Q: Use the Simpson's Rule to approximate the given integral with n = 8. (Find S8.) Round your answers t...

A: Given,∫0211+x6dxHere n=8, therefore h=b-anh=2-08h=14 Now we create table  x 0 1/4 1/2 3/4 1 5/4 3...

Q: Find the slope of the graph of the function f(x) = V3x at (3,3). Then find an equation of the line t...

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Q: lim f(T) = 1, lim f(r) = – 00, I -2 f(-2) = %3D 4- 3- -5 -4 -3 -2 A1 2 3 4 -2 -3- -4-

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Q: In this calculus problem, verify that f has an inverse function. Then use the function f and the the...

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Q: Based on empirical data, scientists have determined the following function that models the height of...

A: Given that: h(t)=3.2t

Q: For the function h whose graph is given, state the value of each quantity, if it exists. (If an answ...

A: We have to find limit Value on the basis of Given graph.

Q: The derivative of the function y = (x² – 1)2 (x² + 2)³ is LA. 2x (x² +2)°(x² – 7) 2x (x² + 2) (x² + ...

A: As we know that; The Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f...

Q: If f(x) = sin(a), find f'(x) Find f'(4)

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Q: Reduce the equation to standard form, classify the surface and sketch it     x2 = 2y2 + 3z2

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Q: 4 dx the integrand is x2 In x2 A) True B) False

A: We can find the answer as below.

Q: 2. Solve each of the following using graphing calculator for 0Sx< 2n. Round to two decimal places. F...

A: Topic:- trigonometry

Q: find the maximum or minimum value of the function  g(x)= 100x^2-1100x

A: The second derivative test  Let f(x)  be the given function and c be the critical point of f. If f"...

Q: Evaluate the following integral: 1 dx 1+ 36x2 Note that an arbitrary constant has been added for you...

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Q: Compute the surface area of revolution about the x-axis over the interval [0, r] for y = 3 sin(x). (...

A: We need to find surface area.

Q: Vx m = (b) Find equations of the tangent line at the point (1, 5). y = Find equations of the tangent...

A: Topic:- application of derivatives

Q: For this discussion I want you to: pick a function find the derivative of the function graph the fun...

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Q: Let w(x, y, z) = x + y+ z where x = sin( 9t) , y = cos( dw dæ dy by first finding dt dz and using th...

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Q: If h(x)= (-2+8x+8x^2) (7x+2x^6+7x^7) then h(x)=f(x)g(x) wher

A: Given that: h(x)=(-2+8x+8x2)(7x+2x6+7x7)

Q: Q2/ Find the distance between the point of intersection of the lines A & B and the point (4,-2), the...

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Q: 3. Given r(t) = 12ti + 5cos t j + 5 sin t k , find the unit binormal vector and torsion.

A: Given that: r(t)=12ti+5cost.j+5sint.k

Q: Wnete to y=2x=1 equotion for Hhe line Pacallel the Doinit 4,9) an and

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Q: Evaluate the following integral: 4 + C dx 2-16

A: Here we have to use the trigonometric substitution for solving the integral

Q: Q#3: a) Evaluate the following integralS sec®x dx by using the reduction formula of cosine. b) Expre...

A: Question no. 3a,Given,           ∫sec8xdx

Q: Problem 1: (1+ cos x) y' sin æ (sin r + sin x cos x – y)

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Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal no...

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Q: or f'(9)- f(9)

A: Follow the procedure given below

Q: 3x+4 > [1] S dx x² +3x+2

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + 9 - 5 lim X-4 x + 4

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Q: Find the equation of the family of orthogonal trajectories of the system of parabolas y? = 2x + C. y...

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Q: Solve the differential equation: (2y+3)y'=-(1-3t²)

A: Given that: (2y+3)y'=-(1-3t2)

Q: If {xn} is a bounded sequence on R. Prove: lim n→+∞

A: Given  sequence xn is bounded  we want  to show that  limn→∞xnn=0

Q: Determine an equation for the line tangent to the function at x-e. O Al y--) TT O B) y--) 1 (x -e) D...

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Q: dt 4е-t — et

A: ∫14e-t-etdt=∫14et-etdt=∫et4-e2tdtlet  et=uthen∫et4-e2tdt=∫14-u2du

Q: Differentiate the function after first rewriting the function in a different form. (Do not use the p...

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Q: Consider the function f(x) = Complete the table below and sketch its graph. |-2 -1 -0.5 -0.1 F(x) X ...

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Q: 7. What is the global maximum value of f(x1, x2) = ln ¤1 + ln x2 with constraint 2x1 +3x2 = 6? Round...

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Q: Let f(x) - 9 sin' a 4 f'(x)

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Q: Evaluate the following indefinite integral | 8 sin(x) – 2 cos(x) dx =

A: We have to find integral

Q: Question Suppose that the piecewise defined function f is defined by S V4x + I, -8x? – x + V13 +75, ...

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Q: cos (a + 8) y= dy Find da dy Immum dx Type sin(x) for sin(x), cos(x) for cos(r), and so on. Use x^2 ...

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Q: Section 4-7 : Triple Integrals in Spherical Coordinates 7. Evaluate the following integral by first ...

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Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

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Q: Divide the numerator and the denominator by the highest power of x in the denominator and proceed fr...

A: Firstly , we can divide denominator and numerator by the highest power of 'x' and then find limit.

Q: SA We have seen that the harmonic series is a divergent series whose terms approach 0. Show that 8, ...

A: Given :∑n=1∞ In1+1nClaim :To show that the series is diverges with limn→∞an=0.

Q: Suppose we need to find an equation of the plane that passes through (1, 2, -2) that contains the li...

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Q: Solve the separable equation using the integral factor  y⁴ y¹ +y¹ + x² + 1 = 0

A: Given equation is y4y'+y'+x2+1=0solve it 

Q: Find the linearization at x = a. y = (10 + x)-1/2, a = 9 (Use symbolic notation and fractions where ...

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Q: 3) The solid S obtained by rotating the region below the graph of y = x about the x-axis for 1 < x <...

A: Given:     y = 1/x    Limit: 1 to infinity