Q6. (i) Given Iog(itt) = tE+ t'-t"+ -.., valid for IEl<1, determine the power serhes for log (+2x ) up to powers of 1+3x and hurite down the radius of convergenc

Q: For each of the following integrals, give a power or simple exponential function that if integrated…

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Q: Given a function f is given by f(x) = 3^(x+1) .  Use Taylor’s Theorem to derive a general two-point…

A: we use Taylor's theorem to derive a general two point forward difference formula.

Q: chen*(5) wave ps.wen & " 1.(4) (^) 你 尝 WP *$.$ s'ta) 109, F"0"

A: Topic:- derivatives

Q: How do you fin nd the derivative

A: We have been given a function and we need to find its derivative.

Q: M 1 {[1 '* . _ (w/wn)²]² + [2¢w/wn] 1/2 2 1²}' ||

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Q: Use the mean value theorem to prove e^x>1+x  ; for all x in R

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Q: Assume f' is given by the graph in the figure. Suppose f is continuous and that f(0) = 0. (a) Find…

A: The antiderivative of a function f( x) is a function F(x), such as d/dx (F(x)) = f( x). The general…

Q: 0.1sin(0.1) find the limit value

A: Given : e0.1*Sin(0.1)

Q: Evaluate the improper integral and state whether it converges or diverges. Show limit notation and…

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Q: 9. After t hours, the number of bacteria, N, in a culture can be modelled using the function N(t) =…

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Q: A)(sin x)/ is convergent or not B){x} is convergent or not

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Q: limit as x---3 for the function (x-2)^11/(3-x) using L'Hopitals.

A: Consider the given function (x-2)11 / (3-x).

Q: Evaluate lim 4^(n)(1-cos(theta/2^(n))) as n approaches infinity.

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Q: Given f'(a) < 0, what do we expect is true for f(a +0.5) ?

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Q: State the Mean Value Theorem. Use it to show that for all x ≥ 0, 0 ≤ tan^−1 x ≤ x. [Hint: Use Dx…

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Q: In(cosh x + sinh x) + In(cosh x – sinh x) = - 1 -1 Leave Question 2.

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Q: Produce the central finite difference formula for the first derivative and apply the same formula to…

A: The central difference formula for the first derivative of a function f(x) is defined as…

Q: "INT" function (alternative name is "Floor" function) returns integer value closest to the Input…

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Q: fle) sinzdz Compute

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Q: Evaluate  f '(3). Also, find the two-point forward difference, two-point backward diffrence and…

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Q: 62. Show that lim n→∞ 1 + X n n 63-78 Find the derivative of th - S e* for any x > 0.

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Q: On which of the following intervals is continuous? (a) [2. +x) (b) (-x, +x) (ce) (2, +*) (d) [1.2)

A: Here we will find the interval where f(x) is continuous,

Q: Find the root within a given interval in the following function by secant method up to 5s (a) In x =…

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