d (4z' +7z+8 2.)- dz Evaluating the derivative using quotient rule:

Q: d 4z3+7z+8, 2. dz 3. dx (x)(3x² – 9)

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Q: cos (82)*da 3. %3D

A: To evaluate:∫cos8x3dx

Q: Find the area enclosed by the x-axis and the curve y= 9 – x². (A) 36 square units B 18 square units ...

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Q: Find the volume obtained by rotating the region bounded by x = y² and ¤ = y around the r-axis. %3D

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Q: - 5x + 7, find f(2). Use this to find the equation of the tangent line to the parabola y = 4x2 5x +7...

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Q: -X olx *2+2x+.

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Q: Use integration by parts to evaluate the integral. sin(In(5x))dx

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Q: 3cot 3t csc2 3tdt 4+3cot 3t'

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Q: 2. Consider the function h(x) = 11 - + x3 a) Find the equation of the tangent line to the graph of h...

A: We will find the equation of tangent line as shown below

Q: fo-Vin° e+2 ln² e+ln@ de

A: Here we have to solve the given Integral.

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Q: Given the series: 25 125 3 + +. 72 12

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Q: [ san28 e tan 20 ,tan 28 sec 2 Bd

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Q: find the dot product of a vector function with itself. r(t) is a curve and the magnitude of r(t)=pi ...

A: Let  u = a i^ +b j^ be a vector functionthe dot product of u with itself is given byu·u = a i^ +b j·...

Q: Which of the following lines is an asymptote of the hyperbola (2- 1) (y+1)2 = 1? 4 9. O 2x +3y-1 = 0...

A: We will find the asymptotes of the hyperbola.Below find the solution in the image.

Q: -3 is The quadrant of cos 5 O Quadrant I O Quadrant II O Quadrant IV O Quadrant II

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Q: QUESTION 1 a) Find the interval(s) on which the curve f(x)= x°(x- 3) is increasing and/or decreasing...

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Q: +0+ dx 3. = TE 1+ x2 -00

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Q: For mumbers 9- 10. Consider the probability distribution of the number of mangoes given below. R PIR...

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Q: 1) The slope of the tangent line to the curve y=2/x at the point (4,1/2) is:   2) The equation of ...

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Q: How could I solve this using shell

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Q: 2. (D³ + 3D² – 4)y = 0 -

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Q: Find the alue of C that satisfied the theorem for the function fCx) = 3+ Jc on the %3D in terval (4....

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Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A 3...

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1) =...

Q: What is a function, in your own words? Give an example to back up your points.

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Q: If f(x) = 5-(3/x)+(1/2x^2), then f'(x)

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant an...

Q: use the vortex (h,k) and a point on the graph (x,y) to find the general form of the equation of the ...

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Q: Complete

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Q: Use the definition of the derivative to find the derivative of, f(x)=6

A: topic - derivatives

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Q: A function F is an antiderivative of the function f if F'(x) = %3D for all x in the domain of f.

A: We have to solve given Questions.

Q: Suppose we have a velocity function and an initial condition for position: 1 1 2t v (t) = r (1) = (0...

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other...

Q: What is the equation of the vector in a Cartesian coordinate system that originates from the origin ...

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Q: xdy − ydx = x^2dy, Solve for D

A: We can solve the DE as below

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A: Given query is to find the the displacement function.

Q: Evaluate (sin t + 1)-1 dt A) sin t - sec t + C B tant + sec t +C (©) tant - csc t + C D tan t - sect...

A: Topic:- integration

Q: Consider the vector field F(x, Y, z) = (2xy, x², 1). (a) By calculating the curl of F, show that F i...

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Q: а. (у* — %3D0 2ху)dx + 3x?dy

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Q: de dx = x(6x - 0) + (3x² –9).1 = 6x² + 3x² -9 = 9x -9 (x² -1) | II

A: We know that derivatives of xn is : d(xn)/dx = nxn-1. And product rule of derivatives is  d(U.V) = U...

Q: af af and ax 'ay L: f(x.y) = (x + y)(2x + y)² Compute %3D дхду

A: Given that: f(x, y)=(x+y)(2x+y)2

Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: (a) sec e = 2 e = degrees e = radians (b) cot e = 1 degrees radians

A: SOLUTION-

Q: puc Find the interval where f'Ex) is concave up Xてーカ = (X) t

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Q: a.) Sketch the solid obtained by revolving the region under the graph of f = x2 about the x-axis ove...

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Q: vis question has several parts that must be completed sequentially. If you skip a part of the questi...

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Q: Find II| y dV, where E is the solid bounded by the parabolic cylinder z = x² and the planes y = 0 E ...

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Q: Setup an integral to find the surface area obtained by rotating the curve y = e" about the line y = ...

A:  Given: y=ex   about the line y=119  with the limits 0≤x≤4.6 To obtain the new limits and the Surfac...

Q: 5. In problems 1-5, by elimination the constant 'a' and 'b' obtain the DEs for which the following f...

A: Note:- this is multiple sub parts question and according to our comapny law we can do maximum 3 ques...

Q: Consider the shaded region R enclosed by the curve y = 6x – x² and the line y =-x as shown in Figure...

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Q: Which of the following statements are true? Statement 1: Angles of 5° and-365° are coterminal. State...

A: To write the statements which are true.