1. Determine whether the sequence converges or diverges. If it converges, find the limit a. an = 3+5n² n+n² b. an - nª 4 n³ - 2n

Q: Consider the following function. F(t) = 3t5 5t³ + 19 Find the derivative of the function. F'(t) =…

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Q: bike company produces bikes. The company has a cost function of C(q) = 2(q + 10)² + In(q² + 16),…

A: Given query is to find marginal cost.

Q: Question 5 let y = 4√, find d²y/dx² O-x(-3/2) O 2 x-1/2) 02 O none of these answers

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Q: An antiderivative ofis Inle* - 11. Which of the following statements about the integral A B The…

A: given  antiderivative of exex-1 is lnex-1A=∫-22exex-1dx

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Q: Differentiate f(x) f'(x) = = x5 x - x + 1 x³ + 64

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Q: (a) Use the Chain Rule to find y' if y = (3x+4)3, then check your solution using another method. (b)…

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Q: 5. g(x) = x-1 x² - 1 and h(x) = 3. 4. f(x) = IV. Find the product of all given functic 1. g(x) = 2 -…

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Q: Let f(x) = In[x(x + 4)5(x² + 6)⁹]. Find f'(x). f'(x) =

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Q: 3 Assuming -x³+4y²-5xy = 0 defines y as a differentiable function of x, use the theorem dx 11 dy to…

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Q: 7. Compute the volume of the solid obtained by rotating the region enclosed by y = x, y = 2, and x =…

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Q: f(x) = mx + b '(x)= State the domain of the function. (Enter your answer using interval notation.)…

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Q: 1 0.253 as follows: Let f(x) = −| 8 Jse linear approximation, i.e. the tangent line, to approximate…

A: Given function is f(x)= 1x and the point is a= 0.253. The equation of tangent line at x=a is y =…

Q: Find f. f ''(x) = 20x3 + 12x2 + 4,    f(0) = 6,    f(1) = 1 f(x) =

A: According to question,Given Derivative,f''x = 20x3 + 12x2 + 4,f0 =6,f1 = 1

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Q: Calculate the cross product assuming that u xw = (-4, -8, -3) (2u + 3w) x w = (000)

A: We need to find out the cross product.

Q: Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: In the question they said without determine the numerical values of the coefficients

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Q: Find MID(2) and TRAP(2) for f -5(1 – e−²x) dx. е MID(2) = TRAP(2) = = Sketch the function f(x) =…

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Q: J(x) || x +1° a) Evaluate f-¹(3) = b) Evaluate (f-¹)'(3) =

A: Topic:- application of derivatives

Q: List what transformations need to be done to transform into .   g(x) = 3- square root of 2-x

A: We need to list what transformation need to be done to transform into the given function from the…

Q: Find the interval of convergence of 27" (x-2)+2 (Use symbolic notation and fractions where needed.…

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Q: Find an explicit particular solution of the following initial value problem. dy 3x - 4y₁ y(0) = 0 =…

A: Given initial value problem is                          dydx=5e3x-4y       y(0) =0 Rewrite the…

Q: If F(x) = f(7f(5f(x))), where f(0) = 0 and f'(0) = 1. Find F'(0).

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Q: II. Find the sum of all given functions. 1. f(x) = 2x and g(x)=x-4 3x-4 2. f(x) = x² + 3x - 5 and…

A: Introduction: Sum of Two Functions: The sum of two functions is found by adding the two functions…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(4r — s, s² – 9r). Use the table…

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Q: dy To calculate: The of function (sin Tæ dx cos y)² = 2 by implicit differentiation.

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Q: Calculate g'(x), where g(x) is the inverse of f(x): g(x) = = X x - 2

A: Given function:- fx=xx-2

Q: QUESTION 1 If F(S) is the Laplace transform of f(t) = cos² (3t+ O 0.56543333333333334…

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Q: Show that f is continuous on (-∞, ∞). if x ≤ 1 if x > 1 On the interval (-∞, 1), f is a polynomial…

A: f(x)=1-x2   if x≤1lnx    if x>1condition for continuty is limx→1+f(x)=limx→1-f(x)=f(1)

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Q: Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The…

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Q: You are given the graph of a function f. Determine the intervals where f is increasing, constant, or…

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Q: Find the derivative of the function using the Chain Rule. 6 GGx) = (y-2)² (y² +4y)* 2

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Q: Find the derivative of the function f'(x) = f(x) = √x² + 8 2 x²-8

A: If f(x)=g(x)h(x) then the derivative of f(x) is calculated using the…

Q: i. Limit Through Graph 1. One example of a graph of a function with a hole. 2. One example of a…

A: The given conditions are, 1. One example of a graph of a function with a hole.2. One example of a…

Q: The (exact) average value of f(x) = ¹ In(x) on the interval (Your answer should be in exact form.)…

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Q: Find the vector and parametric equations for the line through the point P = (-2, 2, 3) and parallel…

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Q: Suppose f(x), f'(x) have the values shown: 0 f(x) 2 f'(x) -7 X Find the following. d dx -In(f(x)) at…

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1 from the we can write…

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = x²cos x, n = 2, C = T

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Q: Find the slope of the tangent line to the graph of the function y=f(x)=−7.5x^2at point x=3 Your…

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Q: "J^² Un= 1 + 1 22 3Q P ++ t na Use 11 -1 1-1 n 12

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Consider the triangle with vertices A(2,3,5), B(-1, 4,4) and C(-2, -1,6). Use vector multiplication…

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Q: You invest $700 in an account in 2005. In 2013, the amount has increased to $819 due to interest.…

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Q: Refer to the transform function £(s). What is the inverse Laplace transform of £(s) £(s) = 20 /…

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