Find y': y = ar cos

Q: Find the derivative. 8 + ex y = In 8 - ex Step 1 The given function y = In 8 + ex can be written as…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

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Q: dx (r-1)%

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Q: V19+r* dt , find f'(C

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Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas…

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Q: x* +x? 5. lim, +* e* +1 In x 6. lim, csc(6x) csc(2x) 7. lim 5x+ 2lnx 8. lim, X+3lnx 2Tan 'x-x 9.…

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Q: Use the below graph of f(x) defined on the interval (0,12] to answer 4 through #9. 4- 11 4) Over…

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Q: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y=…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

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Q: ind V × (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V x (V × F) = ||

A: Topic:- application of derivatives

Q: 6. (ax3+ bx2+cx) dx= 2b | x2dx where a,b and c are constants. -9 A) True B False

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Q: Find an equation of the tangent plane to the given surface z = x sin(x + y) at the point (-1, 1, 0).

A: Given,  z=x sin(x+y) ⇒x sin(x+y)-z=0 Let f(x,y,z)=x sin(x+y)-z Recall: The equation of the tangent…

Q: 2. sin 2wcos 2wchw

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Q: If x=tan , then dr = coso de by trigonometric substitution. (1+x*)½" A True B False

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Q: Find y': y = arctan(e2x) 2e2x y 1– e4x? 2e2x y = 1 – e4x %3D 2e2x y 1 + e4x %3D 2e2x y 1 + e4x2

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Q: Attempt 3 A net is dipped in a river. Determine the flow rate of water across the net if the…

A: Given

Q: Find r'(t). r(t) = (arcsin(t), arccos(t), 0) r'(t) =

A: This question is based on diffrentiation.

Q: Find the particular solution determined by the given condition. f'(x) = x2/5 + x; f(1) = -6 f(x) = =…

A: We can find the particular solution as below.

Q: 2. By differentiation rules , evaluate the derivatives of the following and simplify as possible:…

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Q: Graphs of Logarithmic Functions Formulas for the Graphs 5- a. f(x) = – log,(z) 4- b. f(æ) = log,(x)…

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Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: PART III: APPLICATION 5. a and b have magnitudes of 5 and 6, respectively. The angle between them is…

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Q: Write the sum in sigma notation. 4 3 1. +- 6. 6. 26 | ... 8. 10 12 52 3+n Ce tn an= fram T 26 26 3+n…

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Q: Find div F and curl F if F(x, y, z) = x°i – 6j + yzk. - div F= curl F=

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Q: Find a value for k that will make the given function a probability density function. f(x) = kz, on -…

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Q: Ir(t) - u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = cos ti + sin tj + tk, u(t) = j + tk…

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Q: Find all the first and second partial derivatives of the function f(x, y) = x²y – 3y“.

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Q: 3. For the given differential equation xy' – 4y = x*e* a) Find P(x) and Q(x) functions of a FOLDE.…

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Q: 2. Given the DE as (x² + y² – 3)dx – 2xydy = 0 a) Prove if the given DE is exact or non-exact b)…

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Q: x + 4 1. Evaluate dx. Vr2 + 8.x

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Q: dy Given the equation below, find dæ - 51a" + 7a"y + y10 = - 43 dy 172 (15 – 1422y) 29. dæ Now, find…

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Q: 9. 5+ 8 7- 6- 3 5 4 2 g(x) 2 h(x) 1 1 1 2 3 x-values 4 5 1 2 3 x-values 4 If f(x) = g(h(x)), then…

A: Explanation of the answer is as follows

Q: arcsin = ab' a? - Va? - y?; Find y!. Oy = 2abr(x+b) Va-y 1-y 2ab r Va- 1-y 2ab r/a-y H. 1-2ab z a- «…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x, x = 4, x = 5 and y =…

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Q: Evaluate the integral. V3/2 dr V1- r2 |

A: We know, ∫dx1-x2=sin-1(x)

Q: Differentiate. 10. y = e

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Q: Find the formula for the Riemann sum obtained by dividing the interval [– 1, 0] into n equal…

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Q: Find an equation of the hyperbola having foci at (4, – 11) and (4, 11) and vertices at (4, -3) and…

A: the coordinates of the vertices are  (h , k±a)(4, -3), (4, 3)k+a=-3,…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 4 cos(t)i+5 sin(t)j+ 6tk;…

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Q: Let f(x) : Int dt. Find f'(x).

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Q: 2. C sin $ 2wcos° 2wcw 3. If f(x) = Vi19+r² dt , find f'(3).

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Q: ph of the parabola to fill in the table. 10- (a) Does the parabola open upward or downward? O=0 6+…

A: Given query is to find characteristics of parabola.

Q: Find the Taylor series generated by f at x = a. f(x) = e*, a = 7 Choose the correct answer below. ki…

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Q: Evaluate the integral / (4x + 18y) dx + (27x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

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Q: 422+3r-2 Given z+1 determine y" 18 (z+1) (z+1) 2 (z+1) 10 (z+1)

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Q: 3. Find y" y = vx² – 4 -

A: Given query is to find the derivative of the expression.

Q: dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point.…

A: Given query is to find the derivative and the slope of the curve.

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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Q: y = 4e2x + xe2x; y" - 2y' + 1 = 0. Yes O No

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i – 3x?y?j

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