(4 if x1 = x2 l0 if x1 # X2 The function f (x) = is defined on the set X = [0,2] x (0,2]. (1) Is the set X closed? (2) Is the set X bounded? (3) Is the set X convex? (4) Is the function ff continuous?

Q: -x² + 2x +1 ,x1. If the function f(x) is continuous on Real number, then find values of b and c.

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Q: 1. (Find the value of a so that the function f(x) is continuous everywhere.f(x) ={2x+a if x<1…

A: Given:

Q: 6x -4, xS 5 -kx + 6, If the function f (x) = is continuous at r = 5, then the value of k is --- --…

A: The given function is: This function is continuous at x = 5, if at this point left side limit,…

Q: (kx-1 ifx< 2 G(x) kx? if x 2 2

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Q: 3. Find the absolute maximum and absolute minimum values of f on the given interval. b. g(x) = x +…

A: We will use the fact that at the point of extrema the derivative of the function is equal to zero. I…

Q: 5. Find the global maximum and minimum for the function given below on the closed interval. (a) f(x)…

A: Given the function :

Q: 2. The domain of the function y = 2159 / (k+1 - x^2)^(0.5) where ke R and k> -1, is: a) - (k+1)^0.5…

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Q: 2. Find the value of k so that the function Sa² + 25 |kæ – 40 is continuous at x = 5. defined by…

A: Given,          The function defined by fx=x2+25    x≤5kx-40    x&gt;5           is continuous at…

Q: 1. Find the absolute maximum and absolute minimum values of "f" on the given interval. A. f (x) 12 +…

A: f(x) =  12+ 4x -x2,       [0, 4] f(x) =  x + 1/x,             [0.2, 4] f(x) =  x - ∛x ,…

Q: 2. Find the absolute maximum and minimum values of the function f (x) = - on the closed interval -2…

A: We need to find absolute max and min value in given interval.

Q: x + 4 - is continuous at c = -4 and c = 4. Use limits to analyze the graph of R at c. x - 16 -…

A: R(x)=x+4x2-16

Q: x1 -1 if For what value(s) of x is the function f(x) = x+1 %3D (x² +x+1 NOT continuous?

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Q: 1 The residues of a function f(z) are (:-4)(=+1)

A: Introduction :

Q: 4. Find the constants a and b, such that the function is continuous on the entire number line. 2, x…

A: Topic - continuity Of a function

Q: 4. Sketch the graph of one function f(x) that has all of the following properties: a.) The domain of…

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Q: x² + 2 if x < 0 b) f(x) = ax + b if 0sx<1, (3 + 2x- x2 if x 21 determine a and b, such that the…

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Q: 7. Find the value of the constant k such that the foloowing function is continuous for all values of…

A: Take LHL=RHL

Q: 8. True or False A function f is decreasing on an open interval / if, for any choice of x, and x, in…

A: A function f(x) is increasing if f(x2) ≤ f(x1) whenever x1 &lt; x2. It is strictly increasing if…

Q: 1. Find the value of the constant k such that the function f(x) = kæ² + 3 if x -1 is continuous for…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: The graph of the function is a translation of the graph of f(x) = Vx. Graph the function. h(x) = Vx…

A: We can solve the problem by finding the transformation.

Q: 2:46 Find the value of the constants a and b that makes the function continuous. Define x-1 : x

A: Consider the given piecewise function and the condition for the function f(x) to be continuous.

Q: 1. The graph of ƒ' is shown. y = f'(x) 2 -2 1 1 2 3 4 6 7 -2 -3 Sketch the graph of f given that f…

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Q: 1+x2+y2 Determine the set of points at which the function F(x, y) = is continuous. 1-x2-y2

A: In this we have to check Discontinuity of equation.

Q: a): Find the value of k that makes function continuous at z = 4 (3x +7 z> 4 3x-k I<4 f(x) =

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: At what points is the following function continuous? x+2 y= 2- 7x+ 10 A. The function is continuous…

A: Please refer the attached image for complete solution.

Q: Please show all work

A: Consider the graph of the function:

Q: g(x) f(x) k(x) h(x) Without a calculator or computer, match the function 3", x³, In(x)/ In(4) and…

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Q: Find the global maximum and minimum of the function on the given interval:f(x)=x2−2x+5,x∈[−1,4].

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Q: 5. If fis a continuous function and if F'(x) = f(x) for all real numbers x, then f(2x) dx = (A)…

A: Given that, f is continuous function and if F'(x) = f(x) for all real number x , To find that…

Q: The function f(x) graphed below is continuous, but not differentiable, at 3 2 1 1 3 4 -1 O. *- -I…

A: From given graph it is clear that

Q: 1) Determine the value of c such that the function is continuous Vx E R. Show and explain in…

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Q: Зх-4 (5) Let f(x) x E [-2,2], find the absolute maximum and minimum x²+1 values of f(x).

A: We will find out the required value.

Q: 3. Determine the values of a and b if the given function f(x) is continuous. 1 ,x 2

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Q: 1- x 0<x<1 (2) Find all the points of discontinuity of the function S(x) = } x +2 1<x<3 x 2 3 (x² –…

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Q: 2. Define a function 6x2-x-15 3x-5 f(x) = |k, 3 (a) Find a value of k so that f(x) is a continuous…

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Q: 2. Find the value of k so that the function defined ( x2 + 4 x 2 - x = 2.

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: x2 – 16 This Graph of f(x) = %3D x – 4 4, but the function is undefined at x = limit as x → 4…

A: Given function is fx=x2-16x-4. We know that a rational function is defined if it's denominator is…

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

A: Consider the given function, gx=x+4 over the interval -7, 1 differentiating the above function we…

Q: 2. The equation for a family of functions with zeros at +3, and -1, with end behaviors from Q2→Q4…

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Q: Example 4. Given an interval [a, b] that satisfies hypothesis of Rolle's theorem for the function f…

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Q: 2. The function f is defined by f (x) = x²e-z'. At what values of does f have a relative maximum? A…

A: Differentiate f(x)=x2e-x2 with respect to x and equate the first derivative to 0 to find the values…

Q: x3-1 D. Is the function k(x) = {x²-1* * 1 continuous at x = 1? 2,x = 1

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Q: 1) determine the value of the constant k so that the function is continuous in x = 2…

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Q: 3. Find constants A and B that make the function continuous and differentiable for all x. Ax x > 1…

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Q: 11. The graph of a twice differentiable function, f(x), with a relative minimum at (–1, –2) is shown…

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Q: Find the global maximum and minimum of the function f(x)=√3−2x on the interval [−3,1).

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Q: 3. Find the absolute maximum and absolute minimum of the given function in the closed intervals. a)…

A: For absolute maximum and minimum. we need to check valie of f(x) on critical points and boundary…

Q: A cubic spline S for a function f is defined by: S(x- 1) + b(x - 1)² + 2c(x – 1)³ 13xS2 S(x) = (5…

A: Introduction: The basic concept of cubic spline interpolation is inspired by the engineer's tool for…

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.