- Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: du ap B) Prove that dx n- dx v2 where u = f(x) and v = f(x).

A: To find  d(u/v) /dx

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: dz If z%3D (х +у) In(x + y) then dx

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Q: dy Let y = f(x) such that In(x – y) = 2x – y + e². Find dx

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Q: Is the follwing argument correct? Why or why not? justify your response in detail. To compute S,…

A: yes, the argument is correct.

Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 4x, x = 3, Ax = 0.5 Ay = dy Sketch…

A: In this question we have to find the value of △y and dy.

Q: Show that S f(x,y) dy dx = , f(x,y) dx'dy. %3D

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

A: Explanation and solutions is given below....

Q: - Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D %3D

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Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

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Q: (a) Let I = dx. Show that I² = dx dy. R2

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: +! dy dx x dx A- If Z = d'y x dx x dx? Prove that Z.Z = xp -1% NI X

A: A Given Z=d2ydx2+1xdydx. We need to evaluate Z.Z. Consider Z.Z.…

Q: Evaluate /f/2e(*+у*+ dV over B where B - {(a, у, 2) : а? + у? +2? < 1}. Тake п %3 3. SSS 2e(z²+y° О…

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Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: Consider S dx and using u-substitution in rewriting the integrand as a function of u and du.…

A: topic - indefinite integral

Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: Evaluate the integrand S(2 + 5x)e dx using IBP. A. 5xe – 39e* + c B. 15xe – 39e* +c c. 15xe* – 9e*…

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Q: Evaluate dy/dx when t = 7 such that: y = 2z^2 - 3z + 5 x = 4t^3 + t t = z^2 + z + 1

A: Given                y=2z2-3z+5           (1)    x=4t3+t                   (2)    t=z2+z+1…

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: dy What is the value of dx at the point (1,0) if y = In(x² + y²)? %3D Undefined O 1 O 2

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Scy dx –x dy; C is the cardioid r=1- cos 0.

A:

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: Fnd the differentnad dy of the functen, sh Cx)

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Q: (1) So“ dx let t=x o Vx

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: Use Green's theorem to evaluate f (x²y) dx + y²dy here C is close path formed y = x and y = x³ from…

A:

Q: dy find 3 - x x - 2 1) If y = t + 2t , t = %3D %3D dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dx dy. Evaluate by changing the order 4y

A: In the given question we have to evaluate the integration                ∫01∫4yyex2dxdy by the…

Q: dy If y = e" In(u) and u = V1-x2, Find dx

A: y = eu ln(u)       and   u = 1-x2 dydx = ?

Q: Let y = -. Find dy and Ay at x = 9 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

A: Solve by using differentiation

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.