e2x - e 2x 3. lim, 0 sinx

Q: What is the result of multiplication of complex numbers -V3+i and (cos +i sin )?

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Q: Prove that n2 +1 > 2? when n is a positive integer with 1<n<4.

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Q: 1 :? 5+ x² Which of the following is an antiderivative of the function f(x) : %3D (a) 2x In(5 + x²)…

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Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different ways. dt dt r(t) = ti + 2t2j + t³k, u(t) =…

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Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

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Q: 20. Evaluate the limit lim 213

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Q: -(1/3), 3/9, -5/27, 7/81

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Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: Find the J(2x + 1)³ dx

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Q: 24. (х? + 2х + у) dx + 2dy %3D 0

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Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

Q: 29 The measure of an angle 12 radians is equivalent to degrees. (A 555 B) 465 C 435 D 525

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Q: Evaluate the line integral / -ydx + xdy along the curve C C : y? = 27x from (27, 27) to (0,0). NOTE:…

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Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: sion into quadratic form, ax² + bx + c = 0, and ide %3D

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Q: Evaluate and simplify: 4sin(4)- csc(-) 2 A 1-2/7 B 1+2/7 -1-2/7 D -1+2/7

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Q: Use the Newton-Raphson technique to find the value of a root of the equation e = sin 4x. An…

A: Given:

Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

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Q: 3. Compute f(x)dx 2х if x<1 f(x) = { 4 if x21

A: As we know from the property of the definite integral. ∫abfxdx=∫acfxdx+∫cbfxdx And The Power rule:…

Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Find the e v

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Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: 6. Consider the DERIVATIVE f' graphed below. Sketch a possible graph of the original function f on…

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

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Q: k=0 X n-1 The sequence { Xn}, where n20, is defined by Xo = 1 and Xn= E (xx) for n 2 1. The infinite…

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Q: Sketch a single graph of a function f(x) which satisfies all of the following the limits and values.…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 3. Vdx + (2x +1 – Vx)dV = 0

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Q: +2x-15 Inkx + 51 -inlx- 31 +c In]x+51-Inx- 31+C Option 1 Option 2 |(x + 5)°| +C (*+5) +C *-3 Option…

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Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: 1. Find all relative extrema and soddle points of the functon Use econd Partials Test where appli…

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Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: A _1. (2x – 3) dx A. -2 _2. L(x3 + 2x) dx В. 0 _3. (x² – 2) dx 1 С. 3 4. S(x3 + 3x – 1) dx 2 D. 2 |…

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Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: Use series to approximate | V1+ x*dx correct to two decimal places.

A: Let's find.

Q: Regarding on the letter c, why is it equated to negative gamma?

A: c) The direction ratio of D→-C→ is -2, 5, -5 from part a. D→-C→ is normal to the required plane.…

Q: 1 2 f(t) = 3 Vi+1 2. Given SET A. determine f"(t)

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Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

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Q: b) S X sin xdx 0.

A: Integral by parts:∫uv dx =u∫vdx -∫dudx ∫vdx dxu=xv=sin x∫ vdx =∫sinx dx = -cos x+Cdudx=ddx(x)=1

Q: P1. 18. Which of the following is true? Select one: O a. AxB is the same as BxA O b. If vector A is…

A: Vector

Q: Solve for x. log x = - 4 0.0001 -0.0001 1.386 -4

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Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) =° –…

A: We have to find value of t

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: integration

Q: S 9. Jcosh kt e*dt Ans. s² - k?

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Q: Verify Green's Theorem by evaluating both integrals aN aM dy dA ду ax for the given path. C: square…

A: Application of integration

Q: Find the sum of the infinite geometric series with first term 6 and common ratio 8 S (Round to two…

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