Show algebraically that ƒ(x) = |x − 1| = x = 1. J−x+1 x≤1 (x - 1 x > 1 is not differentiable at

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: Let f(x) = x² – 6x +3 with domain 0 < x < 3. Calculate (f-1)'(-2) . Note: Round to two decimal…

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Q: 2n hニ1 ちn-3

A: Divergence test: Let an be a sequence of real numbers. If limn→∞an≠0 then the series ∑n=1∞an…

Q: Consider the following formula to compute the third derivative of f: ƒ”" (x) = −…

A: The given formula for the third derivative of…

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: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

Q: Consider function P(r) = 470*w (r), where w(r) = e 4 and find it's maximum, i.e. the distance r at…

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Q: Find y as a function of t if 5184y" – 1584y + 121y = 0, - y(0) = 6, y'(0) = 3. y =

A: We have to find the general solution of the given problem.

Q: Suppose f is differentiable and (-1,4) is a point on the graph of f. The estimate f(-0.8) 5 is…

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Q: 2. Find all the derivatives of f, given f(x) = x8 – 5x7 + 4x6 – nx* + 3x3 + 11.

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Use the Second Derivative Test to find the Maximum and Minimum value(s) of the function 3 f(x) x* -…

A: We have the given function as fx=32x2-4x+lnx For maxima/minima, we need to calculate f'x as…

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,…

Q: 1. Let f(x)=√x-2 / x-4 . Show that f(x) has a removablediscotuiti t x=4   2. Given f(x)= √(x+1).…

A: Here we have to find the derivative of a function at a point.

Q: Let f(x) = (x" + 10x) e 6x-5, where n is an unspecified constant. Find the value of n such that the…

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Q: Use the definition of the derivative to determine whether x 2 x, f(x) = is differentiable at x = 2.…

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Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

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Q: Where is the function y =4x/x-3 concave downward? Show mathematical work to clearly answer this…

A: For a given function y=f(x) the curve is concave downward in an interval I when the second…

Q: Owen's house is 12 blocks from the library and 8 blocks from the school. The library is 9 blocks…

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Q: Differentiate the function. H'(z) = H(z) = In c²-2² c²+z²

A: H(z)=lnc2-z2c2+z2

Q: 6. Use the definition of the derivative to show that the function f(z) = Z is nowhere…

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Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Let f(x) = 4x + 5 – 19e“. Then the equation of the tangent line to the graph of f(x) at the point…

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Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: Let f(x) = In(x² – 14x + 52) f'(x) =

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Q: Use the Cauchy-Riemann equation to determine if the function f(2) = x³ – i(2 – y)³ is analytic or…

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