For what value of the constant A is the following function continuous for all real x? if x<1 (Ax + 5 |x² – 3x + 4 ifx² 1 S(x) : %3D

Q: b)f(x) = Vx²

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Q: 1. Find the local extrema of f(x) = x* – 2r2 +1, and state the intervals on which this function is…

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Q: Find the value for k so that the function will be continuous at x = – 1. 9x2 – 18x – 27 +9 if x - 1

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Q: Find a general formula for f (n)(x). f (x) = xe−x

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Q: For what value of the constant c is the function f continuous on (-∞, ∞)? ( cx2 + 2x x3 - cx if x <…

A: We know that for any value of c, for x &lt; 5, the function is continuous and for x &gt;= 5, the…

Q: Given that the function (x+2)(x+1), if x>b-2 -x+4, if x≤b-2 is continuous at x=b-2. If b>0, find b…

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Q: Suppose that f and g are continuous and that f(x) dx = -3 and g(x) dx = 7. Find [E(x) – 4g(x)] dx .…

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Q: ,if x>2 Find the correct value of bb that makes

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Q: (a): Find the value of k that makes function continuous at x = 4 f (x) = 7x S2x + 7 x > 4 k x < 4…

A: We will use the definition of continuity at a point to find the value of k

Q: Suppose that f(x) is a continuous function. | f(2) dæ=4 , then what is the value of [x – f(x)] dx ?…

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Q: 10. What value of k makes the function {2x - (4(x + k) if x > 2 if x <2 f(x) continuous at x = 2? А.…

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Q: Q2-For what value of b is the function x2 - 4x + 4 x # 2 f(x) = %3D x- 2 bx + 6 x = 2 continuous at…

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Q: For what value of the constant c is the .! function f continuous at x-3 |cx – 2 , if x 3 2 -1 -2 1

A: If function is continous then,limx→n+ fx =limx→n  fx = fnat point nso at given point x=3limx→3+ fx…

Q: -3x² + 5x – 12, x 2

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Q: x+k , if x<2 x² +4 , if x22 For what value of k is the function y = < continuous? k =

A: Continuous function. Given function f is continuous if its left hand limit is equal to its right…

Q: If f(x) = L - 3x for 0 < x < 2L, and if f(x + 2L) = f(x), find a formula for f(x) in the interval -L…

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Q: Find the largest interval on which the given function is increasing.

A: Consider the function fx=x-2+1 Since, fx=-x-2+1    when x&lt;2x-2+1        when x&gt;2=-x+3    when…

Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 -4…

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Q: 12. Find the value of k that will ensure that the following function is continuous at x = 3: x² + k…

A: As we know that the function is continuous at x=a if:   limx→a-f(x)=limx→a+f(x)=finite…

Q: For the function S-a² + 2x if x -1' evaluate the left and right limits.as x -→ -1.

A: Given f(x)=-x2+2x         if x≤-1-x2+2x+2    if x&gt;-1

Q: Given the function: x2-4 if x 2 f(x) = , 2-x if x = 2 What should be the value of k so that f is…

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Q: Find a general formula for f (n)(x). f (x) = x−1/2

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Q: Find the value of k so that the function 5x +3 if x<3 f(x) = kx2 if x23 is continuous everywhere?…

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Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

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Q: Find the values of x for which the function is continuous. -3x + 6 if x < 0 (x) = lx² + 6 if x 20 O…

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Q: Find the values of the constants k and m, if possible, that will make the function f continuous…

A: f(x)=x2+5                x&gt;2m(x+1)+k      -1&lt;x≤2   2x3+x+7        x≤-1limx→2+  x2+5…

Q: Given the function: x² –4 if x + 2 f(æ) = { k, 2-x if x = 2 What should be the value of k so that…

A: We have to find value of K

Q: 2. For what values of a and b, the following function is differentiable everywhere? f(x) = {ax + bx…

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Q: Find a formula for f(n)(x) if f(x) = e' -3x fln)(x):

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Q: f(x) = x3 - 3x + 1 = 0 [0,1] %3D

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Q: if x 2 1. Determine the constant k such that the function f(x) = is continuous at x = 2.

A: As per guidelines, I can answer maximum one question. Since you have asked for multiple questions,…

Q: Find the largest interval on which the given function is increasing. a. ƒ(x) = | x - 2 | + 1…

A: Since there are multiple subparts posted, we will answer the first three subparts(a,b,c).If you want…

Q: (b) For what values of the constants c and d is the function continuous and differentiable for all…

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Q: If ɛ ER and the function f(x) = ex – 1+ x² is increasing x E R, show also that e >

A: Since f is increasing hence f'(x) &gt;0 for all x

Q: (b) Find values of x, if any at which f is not continuous (2x +3 xs 4 7+ x>4 f(x) = 16

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Q: For what value of the constant 4 is the following function continuous for all real x? if x<1 [ 4x +…

A: From the given x values , we can see that the function f(x) is continuous at x=1 At x=1 the value of…

Q: At x = 3, the function given by f(x)={x2 , x<3 and 6x−9, x≧3 is? a) undefined b) continuous but…

A: Given function: fx=x2x&lt;36x-9x≥3 Clearly the function is defined on all real numbers. We have to…

Q: For what value of c is the function below continuous at x=-3? f(x) = { c  when x=-3 1 when x = 1…

A: The function                     f(x)=c                       when x=-31                       when…

Q: Find the largest interval on which the given function is increasing. a. ƒ(x) = 0 x - 2 0 + 1 b. ƒ(x)…

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Q: Find the value of k so that the function f(x) =- [ 5x+3 if x<3 is continuous everywhere? kx2 if x 23…

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Q: For what value of the constant c is the function f continuous on (-00,00) f(x) =Cx+4cx+5 ifx<1…

A: Here we have to find the value of constant c for which the function is continuous.

Q: For what value (s) of x is the function f(x)  -4 if  x ≤ -5…

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Q: (a): Find the value of k that makes function continuous at x = 4 %3D S 2x + 8 x > 4 x < 4 f(x) = 5x…

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

Q: Given the function x2 - 4 x<2 X- 2 f(x) =. ax3 – bx +3; 2sx<3 2x- a + b; X23 the values of a and b…

A: It seems that the given options are not correct at all   We will find the correct options using…

Q: If the function defined by 6x + 144 x # -24 g(x) = x + 24 k is continuous at x = -24 x = -24, then…

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Q: The period of the function f(x) = {7 4 for 0 < x < 8 and x for 8< x < 16 f(x) = f(x+16) is

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Q: (x³ + 4, if x 2] Consider the function f(x) = Find the value of D such that f(x) is continuous at x…

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Q: B. Determine whether each of the following functions is (a) continuous (b) differentiable. 12.…

A: Please follow the the explanation.

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.