Differentiate the function. F(t) = tº + e⁹ F'(t) =

Q: (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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Q: Find the limit of f(x) = lim f(x)= -7+- X as x approaches co and as x approaches -8. lim f(x) = X→∞0…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves y = y=0, x= 0…

A: To find:- Volume of solid genrated by curves y=43x+3,x=0,y=0,x=3 about x axis

Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas f f(x) dx…

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Q: (-26)³ 6 If so, write it in the form f(x) = kx². Is the function g(x) The function is g(x) = kx² ||…

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Q: X 16. Determine the equation of the tangent to the curve y=30* at the point with x-coordinate.

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min.…

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Q: 5) Find the divergence of (√x² + y² + z² 5) kî + yî yj + zk)

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Q: Find the length of the loop of the given curve. x = 6t - 2t³, y = 6t²

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Q: you solve the Partial Fraction please

A: Given that             16x2-x+36x3-5x2+1=16x2-x+3(6x-5)x2+1

Q: 6) Show that (2xy, 2yz + is conservative.

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Q: The total cost of producing x magazines is given by the function C(x)=600+17x−0.1x2+0.5x3. Find the…

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Q: Find a Cartesian equation for the curve and identify it. cos(20) = 1 O limaçon Ohyperbola O circle O…

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Q: 8. Determine 16 25 a. b. 4 25 dy dx y = for x²-4 +4 when x 1. Show your work. c. 16 25 d. 1

A: The given function is: y=x2-4x2+4

Q: 28-30) Given f(x) = 2x + 3 and g(x) = 3x + 5 28. If P(x) = f g then P' (2) = 29. If D(x) = then…

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Q: Use Right-endpoint Rule with n = 5 to approximate ²x x√x+2dx to 4 decimal places.

A: INTRODUCTION:  The height of the approximating rectangle is calculated using the right endpoint of a…

Q: 18) The graph of f(x) is shown. fox A) I only 4 B) 1:4 f¹=0 at X = ? c) 1; 4; 5: D) 143536

A: As per guideline only one question is allowed to solve if multiple question is asked in single…

Q: Find the particular solution of the D.E. y "+ 3y + 2y = 4e° = 4e* ON =e* 2 Oy₁ = / = Ae* + B

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Q: 12. Which of the following is a point at which the tangent to y=-xe* is horizontal? Show your work.…

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Q: Find the points on the curve where the tangent is horizontal or vertical. 3 x = t³ - 3t, y = t² - 4…

A: The given curve x=t3-3t, y=t2-4. We have to find the points on the curve where the tangent is…

Q: Consider each function to be in the form y = kx, and identify k or p as requested. Answer with the…

A: Given function:- y=2x

Q: 1) What is the average value of f(x)= e2x over the interval [-5,-2] tan x-sin x 2) Evaluate i) lim-…

A: As per guideline only one question is allowed to solve if multiple question is asked in single…

Q: (a) Show that helpful). (b) Evaluate lim x-0 coth x dx = log sinh x| + c. (Hint: you may find the…

A: Integration using substitution

Q: b) (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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Q: If sin e = V2 and cos e = 4 what is tan 0? 430 O_√7 - 3 4 حرا من 3 O vi 3 - 3 4

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Q: The graph of the function f(x)=25-x² is given below. Which of the following definite integrals…

A: we use integration method to find area given  f(x)=25-x2formula for area is A=∫abf(x)dx

Q: Use the Divergence Theorem to calculate the flux of F across S, where F = zi+yj + zxk and S is the…

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Q: A ladder 15 feet long is leaning against the wall of a house (see the figure below). The base of the…

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Q: 5) ftan5 x sec^x dx = tan6x 6 a) b) tan x 8 tan'x 7 + + tan 5x 5 + + c + c sec7x secx c) 7 5 d) None…

A: To evaluate the following integral.∫tan5x sec4x dx

Q: Question 4 moriro 4. Simplify the following. Show all details and leave your answer with only one…

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Q: Sketch the domain D given by x < 0, y ≤0, x² + y² ≤ 9 and, using polar coordinates, compute [[³y…

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Q: 7. For g(x)=(x² + 7x− 1)*, determine 8 (0). Show your work. C. 0 d. 7 a. -28 b. -4

A: this is question of calculus we have to find the derivative of function further calculation is…

Q: Determine the slant asymptote of the graph of f(x)= x²-8x+14 x-3 Write your answer in the format y =…

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Q: f(x) = (2x³ + 8), (1, 100)

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Q: Determine whether the series given by Σ±% (-3) k+1 (-3)*+¹

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Q: You are attempting to evaluate the integral What trig substitution would you use to simplify this…

A: Given the integral is ∫9x2-9x dx

Q: Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula…

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Q: Find the sum of the first 30 terms of the sequence. 3, 12, 21, 30, ... S30

A: given  3,12,21,30,.....the difference between numbers is 9we know that sum of nth term of a.p. is…

Q: an+1 Find the first six terms of the sequence defined by a₁ = 1 and 5 = an + 1 for n ≥ 1

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Q: 1. Use trigonometric substitution to evaluate the integral √9-x

A: We need to solve integral.

Q: y = 12 - x², y = x² - 6

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Q: Find a general solution to the given equation for t<0. 3 y"(t)- y'(t) + y(t) = 0 ² 29 The general…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: we will find the required.

Q: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

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Q: Convert the equation to standard form by completing the square on x and y. Then graph the hyperbola.…

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Q: What is the exact value of the definite integral?

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute…

Q: Write the sum without sigma notation. Then evaluate. 6 Σ sin kn k=2 Write out the sum. 6 Σ sin kn =…

A: Given series ∑k=26sinkπ

Q: If f(2)= 5 and f'(x) ≥ 3 for 2 ≤ x ≤ 6, how small can f(6) possibly be? f(6) ≥ Need Help? Read It…

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Q: dy 13. Determine the derivative dx for y= -4x 4. Show your work.

A: y= -e-4x/4

Q: X √4- 4+3x² -dx

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