1. find the linear approximation to /(x) at x = Xg. Use the linear approximation to estimate the given number. a) f(x) = (x+ 1)i, x=0, VZ4

Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

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Q: Find the linear approximation L(x of the function f(x) =V1– at a = 0. L(x)=mx+b where m is - and b…

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Q: Suppose that f(x) is a function with f(155)=70 and f′(155)=1. Estimate f(157

A: topic -  line and differentiation

Q: Given that f(3) -2 and f'(3) = 4, estimate f(3.5) using a linear approximation.

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Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

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Q: Find the derivative of the following function. y = In(6x² – 7x) – 4x А) 18х? -7х x(6х* - 7) В) 1 - 4…

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: a) y = −8x² + 4x¯¹ − 2 b) f(x)=√√x - √x 5 c) g(x) = x³

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Q: Find yy as a function of xx if y′′′−8y′′−y′+8y=0 y(0)=4,  y′(0)=−6,  y′′(0)=130.

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Q: Differentiate g(t) = -8/t .

A: Known fact: ddxx=12xddxkfx=kddxfx

Q: Find the derivative of f (t) = (6t3³ - 8t² + 7) 46 f' (t) = BA

A: Given query is to find indicated derivative.

Q: Consider the function f(x)=∫x04t5+4t4−t3+2t2−3t−5dt. Compute f′′(x)

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Q: Let f(x)=√x. By use of the little o notation justify that the linear approximation to f at x0…

A: Given,           f(x) =x

Q: Use linearization to estimate v26. Use L(x) = f(a) + f'(a)(x – a), where f(x) = vx and a = 25. Once…

A: Linearization formula L(x)=f(a)+f'(a)(x-a)