Use differentials to approximate the value of (3.01)2 + 2(0.99) – 3 in four decimal places.

Q: dæ 2 (x² + 1)²

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

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Q: Using Integration By Parts, Vx In 2x dx= uv- Jv du- Find u v- du- 3 x/x In 2x- Vx dx 2 O 2 xVx In…

A: The given integral is: ∫xln 2x dx

Q: 5x dx? x3 + x2 +4x+4 How many quadratic and distinct factors are in the denominator of

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Q: Evaluate the integral [cot5 x csc x dx O 1 1 늑csc? x-cscs x + 하sc3x + C 2 X + x + C 2 esc x + 1 csc?…

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Q: C. ta the sum or the values of a and h such that f(x) - 2ax2 1 hr + 3 has a relative extremum at the…

A: 7.   The function f(x)=2ax2+bx+3 has a relative extremum at the point -1,2

Q: 2x3- x² + x + 2 dx = D dx find A+B+ C+D. + x+1 + Consider x4 + x3 4 O 3 O 2 O 5

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Q: In the diagram below, a and b are vectors such thay cos0 = 1/6. Given thay a= i +j+ pk and b= 2i…

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Q: (2) Problem 2: Use the provided table of values to write the table of values for the following…

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Q: sec(3r2 + In 2) evz+2 +9 a. y =

A: Use simple differentiation formula.

Q: Using Integration By Parts, x Arcsec 3x dx = u v - Jv du - iv- Svau. Jv du. Find uv- o Arcsec 3x -…

A: Given: ∫x Arcsec3xdx=uv-∫vdu   ......(1)   As we know that; The chain rule; fgx'=f'gx·g'x The Power…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let θ denote the angle between thw ladder and the ground

Q: 1 Sxsec - Svdu- Using Integration By Parts, >x tan x- u v- Find UV-

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Q: The velocity of an object is given by the following function defined on a specified interval.…

A: Given  v = 1(2t+2)m/s   for 0≤t≤8 ; n =4 Displacement = ∫081(2t+2)dx Number of subinterval = 4  h =…

Q: | x(5*)dx x(5*) In 5 + C (In 5)? x(5") In 5 5* + C (In 5)² O A x(5*) In 5 + C In 25 x(5*) In 5 + C…

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Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis. Answer:

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Q: dx Using Trigonometric Substitution , find f(e) !! (x2 + x + 1)2

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Q: 1. Evaluate the following limits. 2 - V2a + 10 a. lim 2-3 22 +r - 6 4x – 7 lim с. -1- (3r2 – 2.r 5…

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Q: You’ve started a small business selling handmade keychains. You’ve given one frequent customer the…

A: Here, the given function for the price is: p(x)=10-x2

Q: .3 The result of dx is F(b) – F(a), where F(a) and F(b) are real numbers. What is the value of F…

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Q: x(z+ 2y)100 = yz – x; Zy and xz.

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Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x? + xy + y? - 9x…

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Q: 2x+11 3 1 dx . evaluate Consider 3 dx = x2 + x- 6 1 dx : x+3 - X- 2 x+3 x- 2 X-2 In |x+3 +C x+3 In…

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Q: Find f'(x) and f'(c). Function Value of c f(x) = (x + 4x)(5x + 2x - 4) C= 0 %3D f'(x) = f'(c) =

A: A detailed solution is given below

Q: 3) y = 2 - 3y; y'

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Q: За — 1 (x – 2)(x + 5)

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Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: 1. Evaluate the following limits. 2 - V2x + 10 a. lim 1-3 x2 + x – 6 4x – 7 1 lim с. -1- (3r2 – 2r…

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Q: Use the information about values of the functions and their derivatives to calculate H'(4), where…

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Q: 2x4 + 3x² – 1 (x² – 4x² +5x)? B(2x- 4) + C Rewrite dx as integral of sum of partial fraction D(2x-…

A: Here we have to apply partial fraction.

Q: 2. SET UP an integral which can be used to find the volume of a solid generated by rotating the…

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Q: Let A = (1, 0, 2) and B = (6, -2, 3). Find projaB.

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Q: Find the first partial derivatives of the function. f(x, у) = 3x + 5y + 4 fy fy

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Q: After watching the Section 9.10 vidco, solve the following problen. Make sure that you show all…

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Q: (x3 + у3)dx - 3ху? dy %3D 0

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Q: ind the points of inflection of the graph of the function. (Order your answers from smallest to…

A: Here, the given function is: f(x)=x(x-4)3 So,…

Q: 1. Determine the absolute extrema of f(x) = (sin r – 1) cos r on 2 2 if they exist, and identify the…

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: x2 +x+1 dx 2x2 +2+x³+x

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Q: x2-y는 군.Give the spherical coordingtes.

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Q: Evaluate the indefinite integral. sin (r)cos(r)da + C

A: Explained below

Q: x² + 2x- 10 (2 dx = x² (x² + 4x + 5) (2x + 4) + 1) (2x+ 4) +1) x2 + 4x + 5 x2 2 Consider dx -…

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Q: Se dt

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Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y? - 8x + 16…

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Q: Using the rule of 72, how long does it take for country X's production to double? 19 years Using the…

A: answer is in next step

Q: Find the derivative of the function. f(x) =-4x2+x+ 6

A: Consider the function  f(x)=-4x2+x+6

Q: dx Using Trigonometric Substitution J- 3 sin e+C express the answer in terms of x. (x² + x + 1) 2 4x…

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Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

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Q: A. Direction: Evaluate the limit. f(x) = {x – 2x + 2, x < 2 х- 3, х22 1. Evaluate the limit using…

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Q: 1 Using Integration By Parts, x sec x tan 2 1 -uv-Jvau Find u v- Svdu '2x sec 을x-J25ec을x dx o 1 2*…

A: From the given problem; ∫xsec12xtan12xdx=uv-∫vdu    ....1   We know that; ∫secxtanxdx=secx+C