The most conveneient way to evaluate x2- by substitution is to let Vx2- 4 =y A True B) False

Q: þr+2|dx -3

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Q: Ise Newton's method with the specified initial approximation x, to find x, the third approximation…

A: Solve the following

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds tot = 0. Q…

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Q: For the linear transformation T: R2 → R2 given by a -b a A = b a find a and b such that T(3, 4) =…

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Q: Find the second derivative (y") of the given function: 6. y 2-e -6e* +12e-e" (2-e*)" 6e* (2+e*)…

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Q: 1.

A: Given,  ∫1+∞1xdx

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Q: Define Euler's number e. Sketch the graphs of the function f(x) = at are the domains and the ranges…

A: answer is in next step

Q: Question 1 Which of the following is false? O yofe" = eu . Ine u (x) In e O yof log, u = u' (x) In a…

A: We can solve as follows

Q: For the function, f(x) = 2x – 1, find the inverse function of the given function. а. |

A: Given : f(x)=2x3-1   To Find : Inverse of f(x)

Q: Describe the graph of the equation. r = 9 sin 13t i - 9 cos 13t j

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x²j+ 22²yk. %3D div F=|2 + 12 y² x² + 4 z y curl F=|2…

A: Find div F and curl F

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

A: To determine whether the given statement is True or False.∫-99ax3+bx2+cx dx=2b∫09x2 dx where a, b…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: Given problem:- Find the conservative vector field for the potential function by finding its…

Q: If x= tane, then cost do by trigonometric substitution. dr = (1+x2) ½ True B) False

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Q: 2. Give the domains for the following functions where: 1 f (x) = and g(x) = V4 – x 1 (i) (ƒ og)(x)…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = ellti+etj K(t) ||

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Q: Find the first derivative of the function below: f(#) = cosh(cot(z² – 2x – 7)) %3D

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Q: Find div F and curl F if F(x, y, z) = 4y°z°i – 8a*zl°j – 7xy°k. div F= curl F

A: we have to find curl and divergence of F.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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Q: Determine the vector field of F. F(x, y) = yi - xj

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Q: Find the series' interval of convergence and, within this interval, the sum of the series as a…

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Q: Find V (V × F), if F(r, y, z) = 7e"i+6xe"j – 2ev²k. V· (V × F) =|0

A: We have to find ∇.∇×F→

Q: Calculate xz dS, where S is the cylinder (including the top and bottom) x + y = 16, 0 < z < 5. %3D

A: answer is in next step

Q: EXAMPLE 3 Evaluate the following integral. VI- 4.r2 SOLUTION Let u = 1 - 4x². Then du %3D , SO xdx =…

A: We can solve as follows

Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

A: Let's find.

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: What is dy/dx for va+y+ Vay = 6?

A: Given problem:- What is dy/dx for √(x + y) + √(xy) = 6 ?

Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: / (3V-1)dt is 3- 1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of 3…

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

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Q: Find the limit (if it exists). (If an answer does not exis lim t- 0 e4i sin(9t). + e-6°k 9t

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Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: tanode B В sec®

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

A: We need to show in this question whether the two integrals are equal or not

Q: dr a 2 1 +3

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: -dx is an improper integral. A True B) False

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Q: Given a function f(x, y) = In(9 – x² – y²). (a) Find and sketch the domain of the function. (b) Find…

A: Given function f(x,y)=ln(9-x2-y2 )

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: Evaluate the integral. V3 8 dx /1/v31 + x

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Q: Which among the following is false for getting the derivative of an implicit function?

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y? + z2 subject…

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Q: If f(x) cos-(2x+5) 2, then dom(f) = %3D a+3 (A) (–3, –2) (B) [-3, –2] (С) (-3, —2] (D) (–1,1) (E)…

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: S- 3 dy 3y - sin –+C 4– 9y2 3 A True B) False ||

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Q: Find the foci of the hyperbola. 2-9y-90y-234 = 0

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