Show that the linearization of f(x) = (1+ x)k at x=0 is L(x) = 1+ kx. Iffis differentiable x =a at then the approximating function L(x)= f(a)+f'(a)(x-a) is the linearization offat a. Determine f(0). f(0) = (Simplify your answer.)

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A: Linear differential equation: a linear differential equation is a differential equation that is defi...

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A: according to given figure f-12=6f-15=2f-16=0

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A: The given expression is  log(7x + 6) - log x.   Log rule:   logca-logcb=logcab

Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–10.

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A: Projection of vector u onto v will be: Projvu=u→·v→v→ Therefore, Projection of vector u onto v is gi...

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A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Q. If u = x³tan-1 then x au - +y ay ax au is а. u b. 0 С. 2u d. 3u

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Q: What is the principle root of √6 ? a) 3 b) 6 c) 36 d) 2.44948

A: We have to find principal root of 6. We know that a b=a×b if a and b are positive numbers. Thus we c...

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A: Here given function as fx=6 thus  fx+h=6

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A: rt=2+3t, 1-4t, -4+3t,  1≤t≤6 Now differentiating with respect to t, we get r't=3, -4, 3 Now, r't=32+...

Q: Integrate by parts: Je*sinx dx So

A: The the given integral is, ∫exsinxdx Assume I=∫exsinxdx.

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A: y=-14x+13 Comparing with y=mx+c, we get m=slope=-14 Therefore slope of required line is, -1-14=4   ∵...

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A: Given that AB=-7i+3j+8k   and  A=-2, -3, 6. Consider them as AB=-7i+3j+8k   and  A=-2i-3j+6k. Comput...

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Q: Minimum of a Sixth-Degree Polynomial Find the minimum value of the function f(x) = 2 + 16x + 4x [Hin...

A: Given function is fx=2+16x3+4x6. Let t=x3 So, the function becomes: ft=2+16t+4t2=4t2+16t+2 This func...

Q: Graph the solution set of the system x ≥ 0, y ≥ 0, 2x + 5y < 10 and 3x + 4y ≤ 12 of inequalities ...

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A: Given expression - 6×9×2 = 2×6×9Let,a = 6b = 9c = 2Then we can write given expression as - a×b×c = c...

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Q: Use synthetic division and the Remainder Theorem to find the function value f(x) = x4 + 5x3 + 5x2 - ...

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A: Given: The vertices of a triangle T are O(0, 0, 0), P(1, 2, 3), and Q(6, 5, 4).

Q: Find parametric equations for the lines in The line through P(1, 2, -1) and Q(-1, 0, 1)

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