Suppose that f is a continuous function for which f(1)÷0 and f(t) dt=0. What can we conclude about the function f ? -2 O f(x)=0 for all x's in the interval [-2,2] . O f(-x)=-f(x) for any 0<æ<2. O f(-2) = f(2) = 0. O f(x)>0 for some x's, and f(x)<0 for some other æ's.

Q: Describe the interval(s) on which the function is continuous. f(x) = sec 7EX 8 ..., (-16, -8), (-8,…

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Q: Let f(x) be a continuous function on (-00,0) and f"(x) = (-4x + 5)e4x. The function f(x) has an…

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Q: Determine if the function is continuous at the indicated point 12 1 f(z) = |2|= 1

A: To determine if the function f(z) is continuous at ∣z∣=1, we need to check the following: The value…

Q: 4) (1, 4) 2) (3.-4) (-4, 5) Determine if f is continuous at x = c. (a) x = 4 (b) x = 1 (c) x = -1…

A: Given   The graph of the function  Definition of Continuity :-  A function f is continues at x= c…

Q: Зх-1 13. f (x) = ;(-1,6] х2—7х-8

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Q: 0<x<1 Q.2 Consider the function f(x)= Find x, 1<x<2 and sketch the odd and even extensions for f(x)…

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Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 =&gt; x = 0 and y = 0

Q: Let f(x) = x + 1/2 On which interval is f decreasing? ○ (0, 1) ○ (-1,1) ○ (-2,0) ○ (-∞0, 0)

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Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: Find number k so that f(z) = 10x + 8 x -1 is continuous on (-0,0). O -2 4 -4

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Q: Give an example of an everywhere-continuous function h(r) that is differentiable at every real…

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Q: Find numbers a and b, so that f is continuous at every point.  f(x)= 20 , x-1

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Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

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Q: Show that the function f(x)=x|x| is continuous and differentiable at x = 0

A: To show that f(x)=xx is continuous at x=0 To show that limx→0xx=00=0 use piecewise definition for…

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

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Q: 6. Verify Mean Value Theorem for the function f(x) = 3x² -4x +5 in [-1,1].

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Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: Part 2 Let f be the continuous function defined on [-1,8] whose graph, consisting of two line…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: x2+2x+5. Show, x+2 Q1 Let f: R\ {-2} → R be given by f(x) directly from the definition, that f is…

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Q: The function f(x) = 1/ (x 4 + 6) is continuous for all values of x in R. %3D O False O True

A: We have to determine whether the given function is continous for all values of x in R or not.

Q: Describe the interval(s) on which the function is continuous. (TX) f(x) = sec

A: f(x)=sec⁡(πx4)

Q: Which derivative of f tells us whether the function is increasing or decreasing?What do we check to…

A: Given function ,  f(x) = ln ( x2 + 2x + 5)  Find interval of increasing and decreasing .

Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5

Q: x 4° (1 - - 3x Find the values of A, so that the function f (x) = LAx? + 2x – 3 continuous for all…

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Q: Determine c and d so that f(x) is continuous if 1 x2 + c x + d x -2 C = II

A: Given query is to find the value of c and d.

Q: Find a and b so that f(x) is continuous if f (x) = Ⓒa = ²/1 b = 60 96 a = - ²/2 b = 29/4/20 -²/26 =…

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