Consider the function given by V2 + x x² – 4 x<-2 g(x) = -2

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Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

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Q: Determine the value of a such that f is differentiable at x = 1. for x <1 a sin(x-1)+6 for x21 S(x)…

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Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

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Q: For what x-value (approximately) does the function f(x) = sin(x) – x reach height -2? (Use r = 2 as…

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Q: 9. If f is continuous and 1| f(x)dx = 8, show that f takes on the value 4 at least once on the…

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Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: 2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative…

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Q: Differentiate the following functions using appropriate differentiatio f(x) = (x² + cos x)10 f(x) =…

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Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: Let f(x): e² sin³ (4) x6 sec(x − 2) a. Solve for f'(x) without using quotient rule or product rule.…

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Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

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Q: Suppose that f (x) > 0 for all x, f(x) has a continuous derivative and that е — 1 f(-3) = 0 and f(4)…

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Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

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Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

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Q: Find the absolute extrema of the function on the closed interval.

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Q: Find the value of K that make the functionf continuous at x=2 パ-4 マー3x+2 sin(rx) + kx + k if x > 2…

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Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

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Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

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Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

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Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

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Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: Find a nonzero value for the constant k that makes the function (tan(kx) x < 0 f(x) = Зх + 2k?, x 2…

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Q: Consider the function f(x) over the interval 0, 1. Does the extreme value theorem guarantee the…

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Q: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

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Q: Differentiate the following functions with respect to x (i) f(x) = sin² Vx² + 1 In(x²-3x) sec(7-3x2)…

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Q: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: The derivative of the function f(x) = ecos(2x) + Vex is Select one: O a. sin(2x)ecos(2x) + 2 O b. 2…

A: From the given data: