Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x 0.

Q: Show that the function is continuous. f(x) = x sinx

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Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

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Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Hiwofind the derivative of the function fwith respect to Vaniable t,, tz when ti-l, tz=3 2. X=Lncti)

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Q: SS()dt =x arctan x

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Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

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Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

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Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a ,b],…

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Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: Show that the function is continuous on  (∞ , -∞).

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Q: Find F '(x). F(x) = Jo *sin(x) 5Vē dt F '(x) = ||

A: Topic : differentiation

Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

Q: ( 2x2 , xs1 Dose f(x) = continuous at x =1?why? %3D &+ 1 , x >1

A: Explanation of the solution is given below....

Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: Differentiate the following implicit function with respect to x: xy - -- cos (y*) a.

A: Solving the first part: Given:

Q: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: Find F'(x). *sin(x) 8Vt dt F(x) = F'(x) =

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: In the interval 3 < x < 4 of the first derivative test, f(x) is a. Not moving b. Changes direction…

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Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

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: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

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Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

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: The function f has a continuous derivative. If f (0) = 1, f (2) = 5, and f (x) dz 7, what is %3D %3D…

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Q: True False Suppose f(x) is differentiable at x=a. Then f also continuous at x=a.

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Q: Find a function whose 2nd antiderivative is f(x) = tan(x) + 4x+1

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Q: The actual tracking weight of a stereo cartridge that is set to track at 3 gm on a particular change…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: 5. Is the function given by F(x): = x = -1? Why or why not? Vx continuous at

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: Let f(x) = In(1 + 7 x). Find flS(0), that is the third derivative of f evaluated at 0. f(3 !3D

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Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

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Q: 1 . Let f(r) 2r + 1

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Q: For which  x value(s) is the function  f ( x ) = sin ^− 1 ⁡ ( 2 x )  defined and not differentiable?

A: Given that the function is       f(x) = sin-1(2x)  Here we have to find those values of x, in which…

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.