Determine the sign combinations of f' and f" for each interval A-G in Figure 16. y=f(r) А всD EF FIGURE 16

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A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

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Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

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Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

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Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

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Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

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A: Given that: The graph derivative of f ' (x) of the function f :

Q: 11. Determine the absolute extreme values of the function fx) = 2 cosx- x on the interval 0<x<2x.

A: We are authorized to solve only 1 question, please repost remaining Extrema

Q: H(x) = L, [At) +A-1) ]dt

A: Question derivative of function.

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Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

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Q: 4 Determine the set of x-values where f(x) 12z is continuous, using interval notation. (-x,5) u (…

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Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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A: On solving this we will get

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Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: It appears that f is not differentiable at a = 0. Moreover, the tangent line does not exist at this…

A: yes it is true.

Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

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Q: Find the ninety-ninth derivative of the function f (x) = cos(2x) . O f(09) (x) = 2% sin(2x) f(99)…

A: Let's find.

Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…