Show (in terms of  epsilon - delta ) that a function f : [2 ; 7] follows R be defined by f(x) =square root of (x2 + 1) is uniformly continuous.

Q: If f is continuous but not differentiable at x = c then there is a corner on its graph at (c, f(c)).…

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Q: Consider f(x) = 3|x|, which is in R[-2, 2]. a. Find a continuous function F(x) such that F'(x) =…

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Q: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: Find a constant c such that x² – c2 if x 4 g(x) ={ is continuous everywhere.

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Q: If f(x) is continuous in the interval [-2, 1], ƒ(−2) = −4, and f(1) = -1, can we use the…

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Q: Prove that the function f(x) = 2x is uniformly continuous on R.

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Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

Q: Suppose f(1) is continuous everywhere, and has the following values: 10 20 30 40 f(z) -4 9. 11 3. 7…

A: Given,  f(x) is continuos everywhere  f(x) has the following valuesx010203040f(x)-491137To…

Q: If f"(c)<0, where c is a critical value and f(x) is a continuous function over an open interval I…

A: We have to find f(c)

Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: Consider the function f(x) = In(x + 5) over the interval [1, 9]. Does the extreme value theorem…

A: The given function is f(x)=lnx+5 over the interval 1,9  The extreme value theorem states that if…

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

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Q: Prove that f(x) =√x is uniformly continuous on [0,∞).

A: According to the question, we have to prove that the function fx=x is uniformly continuous on [0,∞).…

Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: Find the value(s) of k that makes the function continuous over the given interval. a < k k < a S 3x…

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Q: Suppose f : R → R is a continuous function with the property that f(x) = 0 for every x E Q. Prove…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: Given a continuous function of which is twice differentiable, if f" (c) > 0, which of the following…

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Q: Suppose that f(1) = 2, f(4) = 8, f'(1) = 10, f'(4) = -3, and f" is continuous. Find the 4 value of…

A: We have to find the value of the given integral.

Q: Prove f(x) = x2+4 is not uniformly continuous on R.

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Q: Given a set E c (0,1) of measure 0, construct a continuous non-decreasing function f : [0, 1] → R…

A: We will use knowledge of measure theory and real analysis to answer this question. As instructed in…

Q: (11) (C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on…

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Q: Suppose that f : R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the 8–neighborhood…

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Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: Prove, if f(x)= V1+x² –In +1+ 1 is increasing and concave on x X E (0;+∞) .

A: f is increasing if first derivative is positive in the interval  and f has concave if second…

Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

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Q: If f : [0, 3] → R is continuous not constant, then its range be a closed, bounded interval?

A: Yes true.

Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

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Q: Define f(2) in a way that extends f(s) = 2 to be continuous at s = 2. %3D -4

A: The function is defined as fs=s3-8s2-4.

Q: Find the value of a such that the function S(«) = {** -1, x < 3 x 2 3 | f(x) = 2ах, is continuous at…

A: Given:      f(x) = x2 - 1  , x &lt; 3     f(x) = 2ax  ,   x ≥ 3

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) &gt; 2      if 0&lt;=X &lt; 1.Is…

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Q: f(x) = x3-3x2+3x-1 ;   m = -1   ;  [-1, 2]

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (a) Prove that if m ₹ N, then the function f(x) = xm is continuous on R.

A: We have to prove that, the function f(x) = xm,   m∈ℕ  is continuous on ℝ.

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

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Q: Prove that if m(x) is differentiable on (−∞,∞) and its derivative m'(x) is bounded then m is…

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Q: Suppose that f(x) is continuous and differentiable, f(2) = -2, f(6) = -6, and f(x)dx =-10. Compute ,…

A: Topic:- Functions

Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

A: Given function is: fx=1+x3 At x0=2 So the linear approximation is: Lx≈fx0+f'x0x-x0…

Q: Determine if f(x)=In (x² + 1) is uniformly continous on the interval I (-0, +0)

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Q: øz (@) is a continuous function of o in the range -o < @< ∞.

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Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.

Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5