Prove the following claim: At least two powers of 3 have exactly 100 digits

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A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

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A: We can find the answer as below using the properties of integration

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A: Given query is to find the total sale for the given time period.

Q: If f(x) = 2x¬1, then f'(x) is equal to a. x2 b. 1 2x C. 4 x3 d. 4 x3

A: Given :   Discontinuity And f(x)=2x-1

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Q: Find the slope of the following curves at the indicated point. 1. y= 4-x? at (3, - 5)

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Q: Question 7 Sslanta 122-9) Identify the correct u A (2y²+3)2 B ® (2+3) © (2y²+ 3) D 4y4+12y²+9 E None

A: Identity the u=2y2 +3

Q: Find the area between 3 and y (a- 1) - 4 with a 2 0. If needed, round your limits of intega %3D and ...

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Q: %23 -2 What is the first derivative of f(xr) = -9(e*)¯² %3D Select the correct answer below: -2x xz-...

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Q: 8. Sketch the graph of a sinusoldal functions with the following characteristice • Domain: • Range: ...

A: from the given data we can conclude that sinusoidal function f(x) have peak to peak value =4time per...

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Q: following questions. (Let each square along the horizontal axis represent 90°. Let each square 2. Gr...

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Q: If F is a continuous on the set of real numbers, then SnF(x)dx = rfFlx)dx (A) True B) False

A: topic- indefinite integral

Q: 3 •(4y++12y²+9) * A (2y²+3)² ® (2y²+3)* © (2y²+3) D 4y4+ 12y2+9 (E None

A: We have to find solution of given integral.

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Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

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Q: (a) State the Integral Test and use it to test the convergence or diver- gence of the series: Σ (1/n...

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Q: a) Verify that the function y = x + x2 is a solution of the differential equation xy' + 2y = 4x², (x...

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Q: Prove the identity. sec x+1 tan x tan x sec x-1 To verify the identity, start with the left side and...

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A: topic - functions and derivatives

Q: 2 -1 -1 67. А %3D 2 1 1 -1 1 -1

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Q: Evaluate the integral. [HINT: Use a shortcut.] 2 12(2x + 1)5 dx 12624

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Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

A: consider numerator series : 3,4,5.........we can re write this as 2+1, 2+2, 2+3 ,............since n...

Q: 81 lim an n→+o The soguonco

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Q: Evaluate by any applicable method. Si VV¤ – 1 dx - 15 32 None of the choices. Please refer to my sol...

A: Topic:- integration

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Q: mor lo1 tan x 47. lim 7/4 sin xr-cos x

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Q: 2x +8 x2 – 12 lim x + 6

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Q: dx Evaluate: Jo JA4-x² ' o V4- O 1/6 O T/2 T/3 O None of the choices ООО О

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Q: -3dy 6. zy2+14y+70

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Q: 6. E yn x" n=1 8.5: 6 Find the radius of convergence and interval of convergence of the series.

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Q: x3 – 1 When you evaluate: dx The sum of the coefficient of for any constant n is 16 7 (c) None of th...

A: We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1   Given: I=∫...

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(-5,-3)

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Q: Suppose that {a, } is a monotone sequence such that a, 10 or increases- in this case we can't say w...

A: We need to choose correct options.

Q: solutions. 1. S(7x³ + 4x²)dx e*dx 2. f 1+e2x 3. S(V1– cos x )dx

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Q: yapi u a ruUI ID yivai. Use ue yrapi u u caui UI Ue IUIUwny. a. The numbers, if any, at which f has ...

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Q: Solve

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Write the correct u and du. 3edx -16 2.10-3rdr ...

A: We need to solve integrals.