At what point on the given curve is the tangent line parallel to the line 3x - y = 3? y = 3 + 2ex – 3x (x, y) = (

Q: onsider the following curve. y = x, 0sx<5 Set up an integral in terms of x that can be used to find…

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A: We know that integration power rule is - Integration of xn is xn+1/n+1+ C  Here C is integration…

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A: To use sigma to write the sum.7n6-7n7n+...+7nn6-7nn7n

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Q: Is 3 A m, m being any real number, possible? Explain. [IC]

A: This is a problem related to vector parts. Based on the general formula and concepts we will answer…

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Q: If an alternating series is not convergent then it is divergent. Select one: O True O False

A: We can find the answer as below.

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: 7. 1. A = 4 6. 4…

A: 1.A=7-346 det(A)=7×6-(-3)×4=42+12=54 2.B=4-5-19 det(B)=4×9-(-5)×(-1)=36-5=31 3.C=213-312-27…

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A: Draw the region and use the washer method of finding the volume of revolution of solids.

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A: Let's find.

Q: 12. Given f (x) = x³ – 12x + 1 (a) Find the intervals on which f(x) is increasing or decreasing. (b)…

A: I have appended the formula used in the solution part.

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A: To write the equation of the hyperbola with center at 4, 2, vertex at 4, 5, one asymptote with…

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Q: Determine whether the series is convergent or divergent by expressing s, as a telescoping sum. 00 n2…

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Q: Suppose z is a function of x and y, and a? – y? = 2"e6y. Solve for dz dx

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Q: 2. Let f (x) = 3 cos(2x) – 1. (a) Find the period and the amplitude. (b) Sketch the graph of the…

A: Use function

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Q: 9. Find the volume of the parallelepiped defined by the vectors. [8, – 3,4] [- 2,9, 1] w = [0, – 4,…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j + k.…

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Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

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Q: whether the selic) H6 use un appropriate test to determine whether the" selics gilon wnverges or be…

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Q: Find the area under the curve y=sin2x from x=0 to x=3pi/4 A. 2 B. 1/2 C. pi D. 3/2…

A: The curve y=sin2x from x=0 to x=3π4

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Q: (3y² + 10xy²) dx + (6xy – 2 + 10x²y) dy = 0 %3D

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Q: Evaluate the integral mx sin nx dx

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Q: 8. Find i • i 55° lū| = 7| = 31

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Q: Evaluate the integral. 18 J xp- 3/2-36 x 18 3/2-36x

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Q: The first along term of a sequence with a (ecursion formila e the lemaing terms for- B given beloN.…

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Q: Convert the following parametric curve into Cartesian form: z = 4 sin t, y = 5 sint O None of these.…

A: To convert the parametric equation into Cartesian equation.

Q: 1 7. (x dy – y dx) = 0 x² + y?

A: We are given a differential equation  1/(x2+y2) ×(xdy - ydx ) =0 We have to determine whether it is…

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A: The given curve,   y=x33+14x, 1≤x≤2

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: Evaluate the integral sec² x tan? x + sec x (sec² x + 1) dx 2 sec x tan x (sec2 x + 1)

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Q: Given f''(x) = 8x + 6 and f'(0) = 1 and f(0) = 2. Find f'(x) =

A: f''(x)=8x +6integrating w.r.t. x;∫ f''(x) dx =f'(x)f'(x) =∫ (8x+6) dx        =8x22+6x+Cf'(x)…

Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…