Use the Ratio Test to determine whether the series convergent or divergent. Σ n=1 Identify an Evaluate the following limit. Since lim 816 n! n" lim 816 an+1 an a an+1 an ? ✓ 1, -Select--- 4

Q: 6) Find the domain of the given functions (use interval notation) and the find f(g(x)) f(x) =…

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Q: 8. Prove: 2 1-tan x 1+tan²x cox2x.

A: (1-tan2x )/(1 +tan2x ) = cos2x here we have to compare the left hand side and right hand side apply…

Q: Find the absolute extrema of the function on the closed interval. h(s) 12 S-5 [0, 1] (s, h) =…

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

Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral = - for…

A: f(t)= t, 0<=t<1          1, t>=1.

Q: Consider the following function. f(x) = x + (-4,-5) (a) Find an equation of the tangent line to the…

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Q: ) . Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: t is a fact that the function  f(x) = x(161/x − 1) has a limiting value. Use a table of values to…

A: We need to find limiting value.

Q: I. Given: 3x - y - 2z = 1 -x + 6y -3z = 0 -2x-3y + 6z = 6

A: The objective of the question is slove the system of equations help of determinant.

Q: If s(t) = 3t2 – 2t – 1, then s(-1) =

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Q: 2x-4 x²-4x+3 1. Express the function f(x) fractions. Find the interval of convergence. = as the sum…

A: Here, the given function is: f(x)=2x-4x2-4x+3

Q: 4. Let g(x) = f(t)dt, where f is the function whose graph is shown. (a) At what values of a do the…

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Q: 24. Differentiate each of the following with respect to x. Simplify fully when indicated 1 (a)_y=x²³…

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Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t) = e-t cosh(t)

A: NOTE: Refresh your page if you can't see any equations. . take Laplace use the Laplace rule

Q: So sin¹ (6x) cos (3x) dx

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Q: 2cosx cos2x+1 3. Prove that secx. Which double angle identity of cos2x did you use and why?

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Q: Evaluate the following integral: [²√²+² (cos(x² + y² S - y²)) dydx

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Q: An even function f(x) for all values of x and x holds a. f(x) = f(-x) b. f(x) = -f(x) c. f(x) =…

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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = {f(t)} and n = 1, 2, 3, . . . ,…

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Q: Consider the function below. f(x) = √64-x² What is the Domain? What is the Range? Enter your answer…

A: Domain of  64-x2 :We must have 64-x2≥0So,  Solution:  -8≤ x≤ 8  Interval Notation: -8, 8

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Calculus II

A: The given sequences, a) an=(-1)nn4b) an=lnn32nc) an=n-knn,  k is a positive constant.

Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: Consider the following. (The graph is called a Witch of Agnesi.) y Find the derivative of the…

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Q: (1) ਤ + x2 x2 + 3 dx (2) In 2 -e ex 1+e dx x +7 (3) --x-6 dx

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Q: Evaluate the following integral or show that it is divergent. 0 -√x VX dx

A: Explanation of the answer is as follows

Q: y = √√2x, x=2 yaxis 17 x-axis

A: Given that y= √(2x) and x= 2 and we find equation of tangent line and normal line at the given…

Q: Evaluate:Z-¹ { ¹(s+2)²-49 }

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Q: 9. Consider the equation 2 5cos x + 4cosx = 1. a. Put the equation in standard quadratic…

A: The given trigonometric equation is 5cos2x+4cosx=1

Q: Find the absolute extrema of the function on the closed interval. f(x) = cos TX, [] minimum (x, y) =…

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Q: Use the Laplace transform to solve the following initial value problem: y" - 2y +26y=0 y(0) = 0,…

A: The given initial value problem is y''-2y'+26y=0, y(0)=0, y'(0)=5

Q: 28.y= I 4+4

A: We have to find derivative

Q: Graph the function given below by moving the vertical asymptote, then the value of the -intercept.…

A: Let's draw the graph.

Q: Find the exact sum of the following series O. In 3 2 1 In(3) --- / 2 In ( ²2 ) 32 3 In (²2) - ○…

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Q: 15. 1/√/2 X 1+ 4x4 dx

A: We need to evaluate :

Q: Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Determine the…

A: Application of derivative

Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =…

A: Solution of given question is written in below steps.

Q: It is a fact that the function  f(x) =  (9x2 − 2) (4x2 + 4)  has a limiting value. Use a table of…

A: We need to find limiting value.

Q: = √ √ XY S: z = 9-x-y, first octant Evaluate xy ds.

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Q: Using the Limit Comparison Test with the geometric series -17, to 8 67 determine if the series given…

A: Limit comparison test -  If we have two series ∑n=1∞an and ∑n=1∞ bn and limn→∞(an/bn) is finite and…

Q: Find the value of the derivative (If it exists) at the Indicated extremum. (If an answer does not…

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Q: Graph the function by setting the x-intercept and the asymptote. Provide your answer below: f(x) z 4…

A: We need to graph the function.

Q: Sandy's main house is a hemispherical glass dome with diameter of 8m. Suppose that the glass is m…

A: NOTE: Refresh your page if you can't see any equations. . the diameter of the hemisphere is 8 m so…

Q: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

Q: Consider the following double integral 1 = ₂ x dy dx. By converting / into an equivalent double…

A: Given :- I=∫-33∫-9-x20dydx convert given integral to polar conversion

Q: A soccer ball is kicked into the air, and its height (h) in feet after t seconds is given by h( t )…

A: A soccer ball is kicked into the air, and its height (h) in feet after t seconds is given by…

Q: dx 3 x + x

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Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, ... an =

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

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Q: dr de sin - r- cos + eª cos = 0

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Q: Use the Root Test to determine if the given series converges absolutely or diverges. ∞ Σα 1 ( 9) n…

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