Theorem 3.1. Let ƒ € C¹[a, b] and 0 < y < x be two real numbers. We have Σ f(n) = = 1₁² f* y

Q: Let 1 f(x) = 2 9, - 2 < x < 5 - The domain of ƒ¯'is the interval [A, B| where A = and B =

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Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: (a. f(a)) is a relative extrema of a function f. When xa, f'(a)>0. (a,f(a)) is O maximum point…

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Q: Find all value of x for the given function defined by y=2x³ – 6x where the tangent line is…

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Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: 3. Find the points (x,y) of the function f(x) = -x³ + 12x² - 5 where the tangent is horizontal AND…

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: 3. Find the absolute maximum and minimum (if they exist) of each function on the given interval.…

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Q: Let f(x) = √6-x The slope of the tangent line to the graph of f(x) at the point (2, 2) is The…

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Q: If f is the function given by ƒ(x) = √²* √t² — t dt, then ƒ' (2) = 7 a. 2√12 b. √2 c. √12 d. 2√12 B…

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Q: Solve for the value of "b" in the equation: * (12) + b 11 Your answer

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Q: The function f is defined by ƒ (x) = -2x³ – x – 5 and f(-1) = -2. If g(x) = f¯1(x), what is the…

A: Given fx=-2x3-x-5f-1=-2Therefore, f-1-2=-1Differentiate with xf'(x)=-6x2-1f'-1=-7

Q: Let f(z) = 3z +2²-9 Determine the value(s) of z, if any, for which f has a horizontal tangent line.…

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Q: A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is…

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Q: (3) (15 points) Suppose f: R→ R is twice differentiable, f'(0) = 0, and |ƒ"| ≤ |ƒ'|. Show that f =…

A: Define g(x)=f′(x). Given the conditions, we have:g(0)=f′(0)=0∣g′(x)∣=∣f′′(x)∣≤∣f′(x)∣=∣g(x)∣To show…

Q: Prove that = eika F (k) dk = F-1 {F (k)} 1 (a) ƒ (x) = (b) F [f (ax – b)] = eikb/a F (k/a).

A: 7. The problems related to Fourier transform are solved as shown below.

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Let f(2) = x* – i(y + 1)°, (z = x + iy), (a) Determine the points where f is C-differentiable, and…

A: Given :-  let f z = x4 - i  y + 13 where z = x + iy (a) The points where f is ℂ - differentiable ,…

Q: 3. Verify that the function f(x) defined over the interval [0, 3], satisfies Rolle's theorem. Find…

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Q: Consider the function f(x) = x ² + 3. Part 1: Compute the slope of the the tangent line to y = x2 +…

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Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: Find ƒ if ƒ' (t) = 5 csc(t) (csc(t) + 2 cot(t)), 0 < t < π, and ƒ (7) f f(t) = = -10√/2

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