Given the function + y-4, find y'. Oy = Oy =

Q: Find the indefinite integral by using the substitution x = 3 sec(0). (Use C for the constant of…

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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: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: Here, the given surface is  6x2+y2-3z2=4⇒f(x,y,z)=6x2+y2-3z2-4 Let, P(x0,y0,z0) be the point of…

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

Q: 3. Find y" y = vx² – 4 -

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

Q: , Evaluate by interpreting it in terms of areas. *P (2* – I^ + *),J

A: We have to evaluate integral by interpreting in terms of area

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: Evaluate the definite integral. (Round your answer to two decimal places.) 1 9 (cosh(x))² dx

A: cos h(2x)=cos h2x +sin h2xcos h(2x)=2cos h2x -1cos h(2x)=1+2sin h2xcos h2x =1+ cos h (2x)2

Q: Differentiate. 10. y = e

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Q: an +1 an +1 an + 1 Recall the Ratio Test which states that, if is a series with nonzero terms, and…

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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: (a) rªr- (b) y2 (c) e-4z+3e7z=3 ,71–3 (d) In(ez)

A: we have to simplify

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: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: Find V· (V × F), if F(x, y, z) = 3ei+ 4.xe®j – 2ev²k. V·(V × F) =

A: We need to find dot product.

Q: Determine whether the series converges or diverges.

A: Solve the following

Q: Find the derivative: 2 (2 + y) = y? O y = y(2-y) z(1+2) z(2z+y) y(1-2) Oy = 2+) z(1-2) y(22+) |3D Oy…

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: Solve the system of differential equations x' 4x – 15y ly' 2а — 7у - x(0) = 3, y(0) = 1 x(t) = y(t)…

A: We solve the given problem using method of elimination by use of operator D  .

Q: Evaluate: /1/T 1–x*dx (A 4) ² +c B D E) None

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Q: Find f and f, and evaluate each at the given point. 3xy f(x, y) = V2x + 2y (1, 1) " (x, y) = 5,(x,…

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Q: 1 Given Rn 7+i- cos 7+ i- , express the limit as n → ∞ as a definite integral, n i=1

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Q: Evaluate the following definite integrals. dr 5. ? +3

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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: Solve the initial value problem y' = xe ; y(-1) = 3

A: We can solve the initial value problem as below.

Q: y= In e+1

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Q: Problem 3 Use the rules of differentiation to to find the derivatives of the function: (a) f(r)= 3rª…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: as (x*ty3) dx -2メydy =0 a.) prove if the given DE is exact or non -exact - Given DE b.) Find its…

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Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: lim 2?e --00 1- cos(2x) im

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Q: Solve the problem. dV The growth rate of a certain stock is modeled by = k(25 - V), V = 20 when t=…

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Q: Find the equation of the tangent line to the curve g(x) = 5x2 - 6x +2 at the point (1, 1).

A: Use equation of  tangent line

Q: 10 8 10 f (x) dr=17 and f (x) dr = 12, then f (x) dx=5. A True B False

A: we use the properties of definite integral

Q: Q2: You have the matrix How can we get the transpose matrix

A: Given problem:-

Q: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

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Q: (b) Using the Power Rule for differentiation, find the derivatives for the following functions: (i)…

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Q: If 39 | f(z)dz = 7 - 89 and - 39 g(x)dx = 25 89 and 39 | h(x)dæ = 32 89 what does the following…

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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: ermine the Interval(s) for which the function is (a) increasing, (b) decreasing, and (c) constant.…

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Q: (2.x+ 5y)dx + (4.x – 5y)dy =

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 y…

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Q: Evaluate the line integral | -ydx + xdy along the curve C : y? = 18x from (18, 18) to (0,0). NOTE:…

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Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy 4+ 12x…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We want (x,y,z) such that 6x2+y2-3z2=4 and ∇f(x,y,z)=λ(2i→+7j→-k→) for some λ where…

Q: Determine the vector field of F. F(x, y) = 9i – 3j

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Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

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Q: Determine if the function is a solution to the given differential equation. y = x In x + 6x + 5; y"…

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