Find the difference quotient of​ f; that​ is, find (f(x+h)−f(x))/h​, h≠​0, for the following function. Be sure to simplify.   ​f(x)=3/x2

Q: The gas law for an ideal gas at absolute temperature 7 (in kelvins), pressure P (in atmospheres),…

A: NOTE: Refresh your page if you can't see any equations. . P=pressure T=temeprature V=volume R, n=…

Q: 40. *3 dx o 5x + 1

A: We will use substitution method to solve the definite integral

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Q: What is the sum of the first 14 terms of the series 9 + 2-5-12-19-...? -25 Ob -98 Oc -511 Od -518

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A: Explanation of the answer is as follows

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Q: (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

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A: Given query is to find indicated derivative.

Q: 12. 30, bag fo sec² 20 de S

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Q: on by parts to evaluate the indefinite integral S 2x sin(x) dx.

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A: According to question,Given Functionfx = x53-5x23

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Q: For which of the values of "a" given below, does lim x-10 exist? Select all that apply. x-ax-10

A: Topic:- application of calculus

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Q: 2. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume…

A: The best place to start is by drawing a diagram. The picture below shows the cylinder inscribed in…

Q: Find the midpoint of the line segment shown below. 5 4 انیا 3 2

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, endpoints…

Q: Use integration by parts to find the following: [(t + 7)e²t+3 dt = Hint: Use the substitution +C…

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Q: Find the x coordinates of the relative extrema of the function f(x) = xe4². Relative maximum at x =…

A: See this solution in below.

Q: valuate the integral f z² dz √25-2² using trigonometric substitution.

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Q: Can you please rewrite the cross product part. I can't understand because of the handwriting. Thank…

A: use the cross product formula. note: it is 29 in third line from bottom

Q: Let f(x) = = f'(x) = - 2 log(x) ƒ' (5) Round to 4 decimal places if needed. =

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Q: Calculate the area of the surface: 20 5 z² = 2 xy with 0≤x≤ 2, 0≤ y ≤ 4, z 20

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Q: If f(x) ƒ'(1) = 6x² + 3x + 6 -, then:

A: Topic - derivative of a function we are given ,f(x)=6x2+3x+6xWe know thatquotient…

Q: Find the indefinite integral. (Use C for the constant of integration.) 6 1.* dx e + 1

A: Given ∫6e-x+1dx

Q: Question 11 Calculate V. v and V x v. v(x, y) = 5yzi + 6 xzj + 4xyk

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Q: 3. Solve the initial value problem y" - 3y + 2y = 4x + e²r, y(0) = 0, y'(0) = 1 by method of…

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Q: Logarithms as anti-derivatives. -5 x (In x)² Hint: Use the natural log function and substitution.…

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Q: Use the principle of mathematical induction to show that the statement is true for all natural…

A: Use the basic principle of mathematical induction to prove this statement.

Q: f(sin³xcosx + sin²xcos³x) dx hint: find gcf (-3 2-

A: sin2x+cos2x=1dsinx dx=cosx∫sinxdx=-cosx+c∫xndx=xn+1n+1+c

Q: (a) Determine if the following series converges or diverges. Σn²-3n+2 00 n=3

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Q: Page 8 of 10 Question 8 Solve the differential equation. ex dy dx + 3exy = 2, x > 0 A) y = ex+e3x, x…

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Q: x cos x dx x sin x + cos x + C x cos x - sin x + C

A: We need to find out the integration of the given function.

Q: The size of a certain insect population is given by ​P(t)=100e.03t​, where t is measured in days. At…

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Q: Use the power series 1 1 + x Σ(-1)^x, x < 1 n=0 to find a power series for the function, centered at…

A: Please see the below answer.

Q: s²+s+1 Exercise 6.4.6: Compute L-1 (2²+ +¹}. $2

A: NOTE: Refresh your page if you can't see any equations. .

Q: Eliminate the arbitrary constants lnw = -x, y = c1w + c2w2

A: Here we have to eliminate the arbitrary constant in the given equation

Q: The solution of the system x - 4y +z = 9 A B D E y - 3z = -1 x = 11m +5, y =3m +1, z = m, x = 11m…

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Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, 3), hyperbola…

A: NOTE: Refresh your page if you can't see any equations. . foci of hyperbola are which lies on the…

Q: Use the tabular method to find the indefinite integral. (Use C for the constant of integration.)…

A: Given integral:- ∫x+82sinxdx

Q: Does the geometric sequence converge or diverge? Explain. 40, -10, 2.5, -0.625,... The sequence…

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Q: Locate all the critical points of the function f(x, y) = 6x - x² 3xy². (If there are several points,…

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Q: (a) Compute 83 of ∞ (c) Use n = 3 and n=1 2 9n6 (b) Estimate the error in using $3 as an…

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Q: 5. Use the Laplace transform to solve the initial value problem. y"+y'-2y=2e³, y(0)=-1, y'(0) = 4

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Q: Find the length of the loop of the given curve. x = 9t-3t³ y = 9t² 6 5 e +39 X

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Q: Find the distance between the points (-1.4,0.5) and (-3.1,1.7) Distance = Give the approximate…

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Q: 5 b [₁² (²x - 7)²¹ dx = [²) vhere = 2x-7 du = 2 7 = -5 = 3 f(u) = 1/10 f(u) du The value of the…

A: Given query is to solve the integral.

Q: dy/dx = 6x^5sqrt(y-1) equals to y = [(1/2)(x^6+c)]^2 + 1? Diff eqn.

A: ∫tndt=tn+1n+1+cgiven  dydx=6x5y-1          dyy-1=6x5dxintegrate both sides

Q: Find the derivative of the function. In(x) y' = y = +6

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Q: Prove or disprove that f(x,y): = x² - y² x² + y² is continuous at the origin.

A: Topic: Limit and Continuity   The answer is given in step 2

Q: Question 10 Solve the differential equation. y' + y tan x = cos X, -π/2<x</2 (A) y=xsin x + c sin x,…

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