3x2 – 1 if x < 0 if 01 Determine c and d so that f is continuous everywhere

Q: Q2/A/ Prove cot² @ csc 0+1 + 1 = csc0 B/Find the value of c if f(x) is a continuous function at x =…

A: To prove the given trigonometric equation and  To find value of c for which function is continuous…

Q: Sx² 1 if if > 2 x f(x) = 5 3 if x < 2 af is differentiable at x = = 2 bf is continuous at x = 2 cf…

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Q: 3x2 – 1 if x1 Determine c and d so that f is continuous everywhere as indicated in the figure)

A: We have given;

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: Q3) For what values of a and b are ax + 2b , y = x? + 3a -b, 3x-5, x 2 Continuous at every x ?

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

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Q: II. Find all values of a and b that make -a -x, x<-2 f(x) = {bx² + 1, Vx + b, -2 Sx<1 x21 continuous…

A: Given:            fx=-a-x,       x&lt;-2bx2+1,     -2≤x&lt;1x+b,       x≥1 Continous everywhere:  at…

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: Ql.a- for what value of (k) is the function y= f(x) continuous at x=2 V7x + 2- V6x +4 -2 sx and x #…

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Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

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: 36 6. If f is continuous and f(x) dx = 2, find xf(x²) dx. %3D

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Q: Зx2 — 1 if x 1 Determine c and d so that f is continuous everywhere

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Q: find constants a and b such that f(2) +3 = f(0) and f is continuouspiecewise f(x) = ax + b , if…

A: We have been given a piecewise function and a condition f(2)+3=f(0) and the fact that f(x) is…

Q: 3. Given х— А ; х>1 f(x) = { 26+x – 3 3B ; x<1 Assume that f is continuous at x = 1. Find the value…

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Q: Q3) For what values of a and b are -x* +а, xsin + 1 0<xs y = bx3 + 2 , Continuous at every x ?

A: Explanation of the answer is as follows

Q: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

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Q: (b) Given -3x + P for x7 Determine the value of p if f(x) is continuous at x=7. TEST DMI123

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Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

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Q: -1.5 0 1.5 For what value of constant c is the function k(x) continuous at x = 0 if k(x)= No such…

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Q: Find the values of c that make f continuous everywhere: ´x² – c² if a 9 smaller c = larger c = Use…

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Q: - f(æ) = Where is %3D discontinuous? x2 + 3x – 18 - o f(x) is continuous everwhere O 3 O-3 and 6 O-6…

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Q: lim f (x) = 4 f(x) has a HA at y=4 418 O True O False

A: From the given problem: limx→∞fx=4 As we know that; To calculate the horizontal asymptotes, solve…

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

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Q: x2- 1 -1Sx<0 1- If f(x) 1 x=0 is it continuous at x=0 %3D 2х 0<x<1

A: Here the given function is  f(x)=x2-1if -1≤x&lt;01if x=02xif 0&lt;x≤1 We need to find weather the…

Q: Q3) For what values of a and b are -х2 +а , x<0 x in+1, 0 < x<- y = bx3 + 2, Continuous at every x ?

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Q: Q3) For what values of a and b are -x² + a , x< 0 1 xsin-+1 , 0 < x< y = bx³ + 2 , Continuous at…

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: Aa 46. Find the values of a and b that make f continuous everywhere. x2-4 if x<2 f(x) = ax? - bx + 3…

A: Given that

Q: Q3) For what values of a and b are (-x² + a , y = { xsin-+1, 0 < xs: bx³ + 2 , Continuous at every x…

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

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Q: 9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

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Q: (3x² -1, x 1, Determine c and d so that f(x) is continuous everywhere.

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Q: |(2x + 1)(x – 2) for x + 2 S(x) = { x – 2 |k for x = 2 Let f be the function defined above. For what…

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Q: 3x? – 1 if x 1 Determine c and d so that f is continuous everywhere (as indicated in the figure) -1

A: Given  f(x)=3x2-1if x&lt;0cx+dif 0≤x1x+8if x&gt;1

Q: Find the value of c so that f(x) is continuous at x = 3? x2 f(x) = x 3

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

Q: Find the number a and b at which f is continuous everywhere? x+a if x 1

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Q: x², if xs1 4. Let f(x) = . Find f. (1) andf'(1). Does f'(1) exists? 2x, if x>1 Show that the…

A: 4. fx=x2,if x≤12x,if x&gt;15. y=f(x)=x2-3x

Q: Q3) For what values of a and b are ax + 2b , y = x2 + 3a -b, 3x-5, 0 2 Continuous at every x ?

A: We will check continuity at breaking points of the function. For continuity , left hand limit and…

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) if 2 s x <…

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Q: Q3) For what values of a and b are (-x² +a, y ={ xsin - bx3 + 2 , 0 <x<: Continuous at every x ?

A: Given information: The function is y=x2+a          x≤0xsin1x+1   0&lt;x≤1πbx3+2       x&gt;1π…

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x 3 a 3D

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Q: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2

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

A: ANSWER : c = 5

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 x - 2 ax? - bx + 3…

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Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

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Q: For all continuous function f: [0, +o] → R, a > 0 we need to prove that 2*f) dx = [ xfw)dx

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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.