cIn2 e*dr = } 1 So Select one: O True O False

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

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Q: Find V · (F × G), if F(x, y, z) = 3ri+j+6yk and G(x, y, z) = xi+ yj – zk. V· (F × G) ||

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Q: Evaluate the double integral. 7x?sin ydA; Ris the region that is bounded by y = x³, y = -x', and y =…

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Q: 7. For what values of m does the function y = e™* satisfying the following equation y" – 3y' – 10y =…

A: We have to find the values of m.

Q: Evaluate F. dr. Jc F(x, y) = 9xi + 6yj C: r(t) = ti + V4 - tj, -1 sts 1

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Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: Find the particular solution determined by the given condition. 3) y' = 7 ; y = 20 when x = 1 A) y =…

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Q: Use the fundamental theorem of calculus to evaluate the following definite integral. | (3x2 + 9) dx…

A: Given query is to find the value of the integral.

Q: Lef foo) the Gempesition (foj)G) 2001 2nd gG6) = e²7#Defermine

A:

Q: 1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the…

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Q: Find the polar coordinates, 0s0< 2n and rs0, of the following points given in Cartesian coordinates.…

A: A)(3,3)r=9+9r=32θ=tan-1(33)=π4tail end of (3, 3) lies in the third quadrant.The polar coordinates of…

Q: x’D² – 2xD+ 2 y=4x

A: Using Cauchy differential equations,

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e10ti + e-*j K(t) =

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Q: The differential equation (xy2 + y)dy = (x + 1)dx is separable. Select one: O True OFalse

A: We have to find

Q: Suppose f(x, y, z) = x2 + y + z? and W is the solid cylinder with height 7 and base radius 3 that is…

A: Given that f(x,y,z) = x2+y2+z2 and W is the solid cylinder with height 7 and base radius 3 that is…

Q: Find out whether the series given below converges or diverges. 00 In (n+ 1) Σ n+1 n= 1 Choose the…

A: Here we will find whether series is convergent or divergent,

Q: If the demand equation is D(x) = 180 - 6.3x and the supply equation is S(x) = 8.2x + 3, find the…

A: If the demand equation is D(x) = 180 - 6.3x and the supply equation is S(x) = 8.2x + 3, then we have…

Q: The figure to the right shows four regions bounded by the graph of y = x sin x: R1, R2, R3, and R4,…

A: To find the value of the  given integral .

Q: Determine

A: Given,             limx→1x2-4x+3x2-x

Q: Find the standard form of the equation of the ellipse with the given characteristics.

A:

Q: Find exactly T(t) and N() for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct answer.)…

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Q: The graph of f shown below has vertical asymptotes at X= - 2 and x = 4. Find the following limits.…

A: Solution is given below

Q: 00 2+n Does the series converge absolutely, converge conditionally, or diverge? 6+n n=1 Choose the…

A: The given series is: ∑n=1∞(-1)n+12+n6+n Let, an=(-1)n+12+n6+n; n≥1

Q: Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. y =…

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Q: Which of the following is NOT a correct way to express the vector v = (2,-4) %3D a) 2î - 4 where î =…

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Q: A particle is moving in a straight line according to the position function s(t) = t° – 6t2 +9t + 5,…

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Q: For the following demand function, find (a) E, and (b) values of q (if any) at which total revenue…

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Q: Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two…

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Q: x³dx U sing trigonometric substitution, is equivalent to

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Q: 25) pind te ered af formed by reusiviny the circie fue su face = 10 cose cbort tue line o= 2 2 a)s…

A: Option C is true

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Find the equation of the tangent line to the curve at the point (5,3) given that x2+xy+2y2=58

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Q: Answer the questions for the following polar equation. 3 r 3= 3+10cos0 (a) Identify the conic as a…

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Q: 10 sin () sin(a da

A:

Q: 3. Use trigonometric substitution to evaluate Sx V9 – x² dx

A:

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: Find the measure of the angle a ircle. 13. (플,-)

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Q: f(r) = Va +4 – 2 Complete the following table and use it to approximate lim f(r) (Round to six…

A: The given function is: fx=xx+4-2   So, at x=-0.1 f-0.1=-0.1-0.1+4-2=3.974841 At x=-0.01…

Q: Use substitution to find the Taylor series at x=0 of the function e -9x. Choose the correct Taylor…

A: Explanation of the answer is as follows

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n5 +…

A: Use alternating series test for checking the convergence of series .

Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

Q: 5y'' + y = 0 y(x) =

A: Consider the differential equation  5y''+y=0

Q: x*dx Using trigonometric substitution, (1+x²) 3 tan ode A sece sin ode B coso tan ode sec20 sec 9d0…

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Q: Зх+1 a) y =- 1 b) g(x)= Vx -

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Q: Find div F and curl F if F(x, y, z) = 11y°z'i – 14.x°z°j – 7xy*k. | div F= curl F=

A: Given problem:- Find div F and curl F if F(x, y, z) = 11y5 z7 i - 14x6 z8 j – 7xy4 k.

Q: Now, differentiate the function y' = 4x(1 + 2 In). y" = 4 + 8 + In + 8 In

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Q: 5) FIND THE MACLAURIN MALLAL fOR SERIES fa)=x cos (2x) %3D

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Q: Find the exact arc length of the curve x = + 2) ? from y = 1 to y = 5. Enter the exact answer. L =

A: Given problem:-

Q: 5. Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 – x} about the x-axis.

A: Surface area