sin'x+8 sinx+16 sin’x+4 sinx

Q: 3 8. f (t) = (10t)z %3D 9. f(t) = tg'(t)

A: Given  f(t)=10t32 To find Laplace transform: 

Q: 6. y = In (e' + e")

A: The given problem 6 is solved below in detail.

Q: True or False: To evaluate the integral dr, 9. we use substitution withz= 3 sec 0, where Select one:...

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Q: 6. Evaluate the improper integral 3dx. Use limits as needed. Give exact 2 answer. . 3

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Q: Carbon decays exponentially. How many grams of the carbon will be left in 123 years, if 161 grams we...

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Q: 2. Evaluate lim -4x+1 X-1 x-1

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Q: Change the order of integration and evaluate the new iterated integral. int _0^1 int _y^1 (x^2 e^(xy...

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Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal...

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Q: t T F(x) = | In(4 - t) cos dt 9. 3 Find F(3) b. a. F'(3) F"(3). You must show your work. C.

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Q: (x+1)' sin x (c) lim- 2x x-0 (d) sinx lim 0 5x 20 +sin e lim (e) 40 бх -sin 2x lim X-0 2x+3sin 4x (f...

A: Using l hospital rule evaluate limit. 

Q: Consider the function f(I)= 6x +5x. For this function there are four important open intervals: (-0, ...

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Q: sec. sec A x2 + 1 x2 +1 2x Option 1 Option 2 x² – 1 x2 – 1 - 2x Option 3 Option 4

A: Given secA+tanA=x To find secA:

Q: y'dx +e* dy = 0 e* +y =c Ans.

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Q: +00 S" x?dx

A: To write that the given integral is improper or not.

Q: Determine the convergence or divergence of the following series. 1 (a) Σ (Use Integral Test.) n(ln n...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: Q 1) Find an antiderivative for each function. 4+ /i a)

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Q: Given that n21 and xn = V5n2 + 2n -3n 00 1. Will {xn}, be divergent or convergent? 2. Will E=1Xn be ...

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Q: CHAIN RULE DERIVATIVES Date Directions: Differentiate the given functions. 2.) G(X) - T52"

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Q: 1. y = x - x'cosx + 2xsinx + 2cosx 2sim x-1 2. y= cosx+2 3. tan(xy) + xy = 0 4. y= x 5. y = xArctanx...

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Q: Find Vlak| for the series. k k k + 12 k=0 (Express numbers in exact form. Use symbolic notation and ...

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Q: n (a) an = (-1)" n+1 (b) an Vn +1 In(n®) (c) an = 2n

A: This is a problem of series and sum calculator. By using several available method we will determine ...

Q: 2. 5x 2 -4 [4, o) )(-00, 1] or [4, o) D[1, 4] )(-0∞, 1]

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A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: The sum of squares of two consecutive odd numbers is 130. Find the sum of the numbers. Let: x = 1st ...

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Q: 1. Consider the curve of the function f (x) = 2x² a. Find an expression for the slope of the curve a...

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Q: 2sim x-1 -y = COST+2

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Q: The number of solutions to cos 0 = – c, with 0 < c < 1 and O 2 Infinitely many

A: This question can be solved graphically.

Q: dx Vx

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Q: =[in(4-x cos (r4

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Q: Sketch the level curve of the function y? f(z, y) = %3D 9. 16 for c = 1.

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Q: Evaluate the integral x Inx dx Select one: Inz -+C Oi In r- a +c 0 in z- +c 3. a Ina O None of them ...

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Q: If 0 be a positive acute angle satisfying cos² 0 + cos“ 0 = 1 then the value of tan² 0 + tan“ 0 is

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Q: Find the open intervals on which the function f(x) = ax² + bx + c, a ± 0, is increasing and decreasi...

A: Given f(x) = ax^2+bx+c, a is nonzero differentiate withe respect to x df/dx = 2ax+b for increasing d...

Q: d²x dx + k?x = 0,k is real number; when t = 0,x = 0, = vo. dt dt2 vo sin(kt) ANSWER: X k

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Q: Evaluate the integral. Answers should be expressed as an integer (no decimals), no spaces, no units....

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Q: A sample of radioactive material starts with 0 grams . After 3 half -lives have passed , how much ra...

A: Let's find. 

Q: +00 n Σ n² + 2-n n=1 WI

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Q: Given the series 2-1 Lx=1 (1+ln²x)x 1. Justify if the series can be proved using the integral test g...

A: Given problem:-  

Q: 16-x2| (a) lim (2 + x) 16-x²| ズ→4+ 4-x

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

Q: Find the three positive numbers whose product is 27 such that their sum is as small as possible.

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Q: 10. f"(t) + 3f'(t) + 2f(t) = 0; ƒ (0) = 1 and f'(0) = 0 %3D %3D

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Q: Q 1) Find an antiderivative for each function. S dt : a) S (1 – cot? x) dx b) +2) dx

A: We know that,  Int(x^n)=x^n+1/n+1+c And, Int(1/x)=log|x|+c

Q: 1. Sketch the graph of the following Quadratic function f(x) = (x- 1)2 -4 and find the following (a)...

A: Given Quadratic Eqaution :  y= (x-1)2-4 Graph : 

Q: Find the open intervals on which the function f(x) = ax? + bx + C, a0, is increasing and decreasing....

A: f(x)=ax2+bx+cf'(x)=2ax+bcritical point:f'(x)=02ax+b=0x=-b2aFor a&gt;0,f is increasing on (-b2a, ∞)be...

Q: Let (P) be the surface given by the following equation + 4 and (Q) be a surface given by the below f...

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Q: d: (a) lim ズー2 オー2--(*+1)

A: Answer:  The solution is as shown below:

Q: 3x dx 1. S 2x 4-1

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Q: Consider the points A(1, -1,4), B(2,-3, 2), C(-1, -2, 2), and D(4, 3, –6). (a) Find the volume of th...

A: The answer is shown in step 2.

Q: Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is R6 (the Right-Hand...

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