sin(bx) x< 0, Q3. Let f(x) = exp(5 + x) х>0. Find a value of b such that f is continuous, or explain why no such value exists.

Q: [sin (zx), 0<x<1 lax+b, 1<x<4 17. Let f (x)= { f(x) is Find the values of a and b such that…

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Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: Determine the maximum and minimum values of the function f(x)= ex cos²x on the interval x= [0,2π].

A:

Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x&lt;πmx+b,      x≥π Since the function fx is continuous…

Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: So, 0, -T < x < 0 f (x) = sin x, 0 < x < T

A:

Q: 1. Find the value/s of b such that the function f is continuous everywhere. x3 + 2, x 0

A: In the question we have to find value of b.

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)…

A: given , f(x)=x+22-3      for x&lt;1asinx-1+6      for x≥1 we have to determine the value of "a" such…

Q: If f( x ) = sin (x) – e“ , what is f'(x) ? O f'(x)=- cos(x)-e² — сos(2) —е* O f'(x)=sin (x) –e² O f…

A:

Q: If f isa differentiable function satisfying f(0) = 0 and f (0) = 2, then 1- cos( f (x)) lim x-0 A) 0…

A: The given limit is, limx→01-cos(f(x))x2. Note that, the given limit is of the form 00. Apply L…

Q: a. Let ƒ(x) be a function satisfying 0 ƒ(x) 0 … x2 for -1 … x … 1.Show that ƒ is differentiable at x…

A: The differentiability of the function can be determined with the help of the left-hand derivative…

Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

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Q: The cdf of a continuous RVX is given by 0, x < 0 sin(Ax) F(x) = + 6x, A 0<x < 2A ° 1, 2A Find the…

A: The CDF of continuous random variable X is given by, F(x)= 0…

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

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

A:

Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

A:

Q: Using FPI, find a critical point of the function: f(x) = x2 – 2e* cos x With an initial guess, xo…

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

A: The local extrema of a function can be obtained by equating the first derivative of the function to…

Q: -x² +1 1- sin? x if x20 if x <0 Let f(x) be defined as f(x)= • Is f(x) differentiable at x = 0? • Is…

A: Answer and explanation is given below..

Q: Find the open intervals on which the function is increasing or decreasing           f(x) = sin x +…

A: Given,

Q: (sin x - a ((x) = {cosx +b -nsx<0 e -1 x<-T x20

A: Topic = Continuity a=2 b=-1

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. Prove that h' is not differentiable at x = 0. .

A:

Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

A:

Q: 3. Find the constant "a" such that the function is continuous on the entire number line. 4 sinx x< 0…

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

A:

Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

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

A:

Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?     3/8…

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Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

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Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

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Q: Find the constant a such that this function g(x) is continuous on the entire number line.

A: Given,

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

A:

Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: It is given that if f is continuous and ∫02f(x)dx =6 The objective is to evaluate ∫0π2f2Sin θcos θ…

Q: Let f(x) Then f'(x) = 3 sin x 6 sin x + 2 cos x m = The equation of the tangent line to y = = f(x)…

A:

Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: The function f(x) sin x + cos x is an even function. True False

A:

Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.

Q: Find the relative extrema of f(x) = 1/2x − sin x in the interval (0, 2pie ).

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: Evaluate f(x) dx, where 8x', ={ 7 sin(x), 0<x< a. -T < x < 0 f(x) :

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Q: dx For = In[F(x)]+C•What is f(/3) if C = 0? (x+x³) (x Tan-lx+ 1) -1 + - - 3. -1 + - + S-is-isS

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Q: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) >= 0 for x element…

A: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) &gt;= 0 for x element…

Q: 5. Given F(x) tan(t) dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

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Q: 1. Find the value/s of b such that the function ƒ is continuous everywhere. f(x) = {6x – sin bx 0 <x

A:

Q: Find the value of c that makes the function continuous at x = 0.

A: Given function:

Q: Find the absolute extrema of the function on the closed interval.                         g(x) = 2x…

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Q: A pdf is given by 2 cos (x 3 ").0<x< f(x) = 3 Show that this is a valid pdf and then find P(X<1).

A: Topic:- probability

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

A:

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.