Let f be given by if x < 5 { sin x 4 f (x): if x > COS x Show that f is continuous everywhere.

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

A: To determine the critical values of a function, dfdx=0 Thus, differentiating f(x) w.r.t. x-…

Q: Determine if a function f : [0,2π] →Rdefined by f(x) = sin 2π is continuous.

A: Given function is f :[0, 2π]→R, f(x)=sin 2π

Q: let f(x)= cos(x)-sin(x)/ h(x)ex, what is f'(x)?

A: Find f'(x) fit given f(x)

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x&gt;0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: Let f(x)  = tan x . Show that  f(0)  = f(π)   but there is nonumber c  in  (0, π)such that f'(c )…

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Q: On which interval is the function f(x) = tan x² continuous Is the function f(x) = ! - continuous at…

A: 3.1)  tan x2 =sin x2cos x2We know that sin x2 and cos x2  are both continuous functions.Thus, tan…

Q: f (x)=, 1- sin x

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Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

A: Note that the domain of g(x) is all real numbers and the domain of h(x) is also all real numbers. So…

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: fx=sinx-1, 0&lt;x&lt;2π To Find: Increasing and decreasing function.

Q: Let f(x) = x cos(3x). Find f' 3

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Q: Is the following function continuous on (-∞, ∞0)? sin x if x x14

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Q: 2. Determine if a function f : [0 ; 2pie] → R defined by f(x) = sin 2pie is continuous

A: Determine if a function f : [0 ; 2pie] → R defined by f(x) = sin 2pie is continuous.

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = sin x − 1, 0…

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Q: What is special about the functions f(x) = sin x - 1 x + 1' x 2 0, and g(x) = 2 tan Vĩ? -1 Explain.

A: Given that functions are f(x)=sin-1x-1x+1, x≥0 and g(x)=2tan-1(x). The graph of the function…

Q: Let f be defined piecewise as follows: kæ sin(x – 3) + 4, if ¤ < 3 f(x) = I – 3 4x2 + k, if æ 2 3…

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Q: find the X values if any at which f is not continuous fx=4x^2-cos(pix)

A: We have to find value x if any at which f is not continuous  f(x) = 4x2 - cos(πx)

Q: sin 219x Is there a value of n that will make the following function continuous at x= x+0 f(x) = {…

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Q: Determine values of a and b that make the given function continuous: if x 3

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Q: If f(x) = 4x sin-), find f'() = f' (0.4) -

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Q: Write the interval of continuity for the function below: tan(sin(x)) log3 (7) f(x)= = for 0 < 2T

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = -2…

A: Differentiate the function f(x)=-2cos x-x with respect to x to obtain the value of f'(x) and equate…

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: Find f'(0) if f (x) = In(cos .x).

A: we have to find f'(0)

Q: Let f(x) f'(x) = = 1 (6 sin x + 2 cos x)tan ¹x

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Q: Find the value of parameters € and ¶ that makes f(x)=€x+¶ if x&lt;0 and f(x) =2(¶+€)sin(x) +…

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Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

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Q: Let f(x) = 8 sin-! (x*) s'(x) =|

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Q: cos x if x 0

A: We have to find the reason

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: Let f(x)={tan(2x) ax+b if x>0 if x<0 For which values of a and b is f(x) differentiable for every…

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Q: What is the largest interval containing zero on which f (x) = sin x is one-to-one?

A: A function f: X -&gt; Y is said to be one-to-one, if the images of distinct elements of X under f…

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: Let f be defined piecewise as follows: kæ sin(x – 3) f(x) + 6, if x 3 For what value of k is ƒ…

A: Given,         f be defined piecewise as follows :         fx=kxsinx-3x-3+6 , if x&lt;36x2+k , if…

Q: Use the concept of composite functions to explain in detail why h(x) is a continuous function when…

A: Composite function

Q: If f(x) = x°cos-x , find f '(x). COS X %3D

A: Given,          fx=x2cos-1x

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: (폭), Let f (x) = x5 sin- Then %3D f'(x) =

A: Given that, fx=x5arcsinx27To find f'(x)

Q: f(x) = (sin x – 1) cos x on 2'2.

A: I am attaching image so that you understand each and every step.

Q: Consider the functions f(x)= x3-1 and g(x)=−2x+sin(x). Show that there is exactly one C in (−∞,∞)…

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Q: Explain, using Theorems 4, 5, 6, and 8, why the function is continuous at every number in its…

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Q: Find f'(x) if f(x) = f'(x) = 8- cos x 8 + sin x

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Q: Let f be a differentiable function. If h (x) = (2 +f (sin x)) ',which of the following gives a…

A: Derivative: - The spinoff formula is one in all the foremost elementary notions in calculus, and…

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.