Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

Q: cot vo csc? Vo de 3 Vo² (4 + cot² Ve)

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Q: 2x2+x - 1 Evaluate -dx using method of partial fractions. Which of the following is the correct form…

A: We can proceed as follows

Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

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Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: 7 -4 Consider the surface x'z* + sin(y zª) + 9 = 0. Use implicit differentiation to find the…

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Q: Given: dx x3 Using trigonometric substitution, solve for the integral form in terms of 0.

A: This question can be solved by taking x=3secθ

Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = In(x2 + 3x…

A: I am attaching image so that you understand each and every step.

Q: What are the domain and range of functions? a) f(x) = cos^(-1) (In(tan x)) b) y= In( (x+1)/(x^(3)+1)…

A: Logx is define for all positive x.

Q: If you are going to evaluate the integral f dx using trigonometric substitution, the answer is 2(tan…

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Q: Consider the following function. f(x) = x3 – 3x2 - 9x + 5 Find the first and second derivatives.…

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Q: 5. sin (2x) dx

A: To evaluate: ∫sin22xdx ⇒I=∫sin22xdx We know that 1-cos2x = 2sin2x

Q: Consider the following function. f(x) = x3 - 3x2 – 9x + 5 Find the first and second derivatives.…

A: Since, you have posted question with multi-parts. As per guidelines, we"ll solve only first three…

Q: ta the téduction of order melhod, the substitution y= 5u can be used for the DE: - 3y/= 0, to obtain…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Differentiate. g(x)=x°cos x

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Q: Find the tangent to y = x-x+10 at x 3.

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Q: You are building a right-angled triangular flower garden along a stream as shown in the figure. (The…

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Q: 00 Given: (1 + 2x)e*dx̟ Using integration by parts and letting dv 00 is %3D u = -1 - 2x, then the…

A: Let's find.

Q: 9. Evaluate limf(x) = {"_ (x – 2; x 3 %3D x-3 а. 1 b. -4 с. 3 d. Does not exist 10. Evaluate limf…

A: Our Aim is to evaluate the limit of the expression given below:-limx→3 f(x)=x-2 ; x≤3-4;…

Q: x arcsec x dx ? xdx A. x Arcsec x - 25- ... B. ** Arcsec x -- V-1 xdx xdx C. x Arcsec x + 25- xdx D.…

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Q: Consider the statements: P:= Today is Monday. Q:- Amy has no classes. R:= Tomorrow is a busy day.…

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Q: dx If x2 - 2x - 4 is solved by trigonometric substitution, which of the following substitutions is…

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

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Q: 3x + 7x + 28 -dx x² + x³ + 7x Using partial fraction, evaluate

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Q: By about how much will g(x,y,z) = x + x cos z -y sin z + y change if the point P(x,y,z) moves from…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: +00 dx -Evaluate the improper integral x (In x)²

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Q: 2. A solid right cylindrical cement block of volume 97 ft³ is to be made, and then painted except…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 2 1 lim t++00 \ 5t2 + 6'4t (?, ?)

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Q: 4x3 + 4x? – 2x + 4 dx - (x² + 1)?

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Q: x e2x dv

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Q: 4. y²tan y

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Q: Find the partial derivatives of the function V1r2 + 1s² + 6r² w =

A: Given,  w=1r2+1s2+6t2

Q: x³ + 6x² + x +2 dx? How many quadratic and distinct factors are in the denominator of x³ +1

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Q: dy Do not simplify your answers. de 3. Solve for sec(3r2 + In 2) eVz+2 +9 c. r Cos y = - log(2³ + y)…

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Q: x² –9 dx Given: r3

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Q: Evaluate. Submit your solution in google classroom sec* 2t dt tanº 2t O -1/(12tan^6 2t) - 1/(16…

A: find the integration

Q: Question- Let R be the region bounded by y= x+2, y30, and x=3. Then draw the region and evaluate the…

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Q: Find the sequence of partial sums S,, S2, S3, S4. and S5. 7 7 + 4 7 7 Σ = 7+ - 1 16 64 256 n = 1 S1…

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Q: Let C be a curve that is defined by x = 4 sint and y = cos t, t e [0, 27]. Determine (a) the time…

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Q: Moha Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y x and %3D y = x2.

A: The objective of the question is evaluate the given integral.

Q: Evaluate the definite integral. esin (a) cos(x) d x

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) (x) = xe8x (a) Find the…

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Q: J sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) , sin(2x)cos(2x) , sin(2x) + + C 12 8 8 4 sin(6x)_ sin(2x)…

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: ∫f(x) dx=∫ 5-31+x2-1dx=∫ 5dx-∫ 31+x2-1dx=5x-3arctanxAdd a constant to the solution=5x-3arctanx+C…

Q: Find the area: y = sin x, the x-axis, the y-axis and the vertical line x = 2 *

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Q: x = 1– t- t - te [-2,2] y =t – t3

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Q: Use the properties of infinite series and the fact that Σ 1 1. 1 and 4 5" n = 1 6' n = 1 5 to find…

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Q: V14 _13. Given the function f(x,y, z) = e3xyz sin 2xy where x = r² + t² , y = t² +r , z = r+t. Then…

A: Given f(x,y,z)=e3xyz sin2xyx=r2+t2y=t2+rz=r+t

Q: What will you factor out from the integrand of csc°(3x)dx so that you can transform it to its…

A: the given integral,         ∫csc6(3x)dx