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: :-3 ifx 2 -3 2-1

A: The given piecewise function is,t(x)=-12x-3if x&lt;2-1if x≥2

Q: g(x) = x³ + x? - 8x- 12 f(x) = x² + 4x +3 %3D h(x) = x² + 3 %3D s(x) = x² - 3x

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Q: If c is a non zero constant then the function is always differentiable x2 + c2

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Q: f(x) = -7x + 6 x² +6 if x < 0 if x 20

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Q: For which a is each of the following functions defined 2x – 3 (a) f(x) = (b) 1 g(x) = 3x + 2 4.x + 5

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Q: Use f(x) = 5x – 3 and g(x) = 4 – x2 to evaluate the expression. (a) (fo n(-1) (b) (g o g)(-1)

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Q: Given the function ( 7x – 4 r 0 |

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Q: . If f f() dr 17 and | f(x) dr = 8, find f(x) dr. %3D

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Q: Consider the following. 4x A(x) x2 - 3x - 4 (a) State the domain of the function. O all real numbers…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Graph the following piecewise functions. IS-2 Sx+ 2 f(x) =-x+3 = {**: x>-2

A: We can answer first question as per the honor policy. Please resubmit other question as well to know…

Q: Identify the real number at which it is not continuous of the given function

A: To find: The real number at which the function is not continuous: Given: The function is fx=-x23x+9.…

Q: Let fx) - 2x-5 and let g(x)= 4x +1. Find the given value. flg(- 2) flg(- 2)] = (Type an integer or a…

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Q: Question 9 Ay f (x) =< ; Estimate f (-2) %3D 8-6 4 O -1 -2 O None of these 2]

A: The graph of the function crosses the x-axis when x=-2. Then, the value of the function at x=-2 is…

Q: (i) Show that we can add and take scalar multiples of the vectors in So and we stay in So. (j)…

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

Q: If 10x³y* + e*Y = 5 defines y implicitly as a function of x, find y.

A: Using derivatives of implicit function.

Q: If f(x) = 3x3 + x. Find f () 6/8 O 5/8 O 7/8 4/8

A: From the given function: fx=3x3+x

Q: 4x + 5 + 5x² – 3 x>5 g(x) =' h(x) =Vĩ - 7x x=5 9x? f(x) = 3x² – 5x +7 4х — 9 x<5

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Q: The cost C in dollars of manufacturing x bicycles at a production plant is given by the function…

A: topic- application of derivatives

Q: 2 V1-x*

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Q: Specify the symmetry of the following functions: 10 (d) 0(x1, x2) = e-l#il X2+3

A: We need to find the symmetry of the function in part (d). We know that a function f is symmetric if…

Q: For what value of x does the function g(x)=-1/3x3 +2x2  convex

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Q: For what x is x(2x+3) positive?

A: For f(x)=x(ax+b). (1) f(x) is positive: ⇒x(ax+b)&gt;0⇒x&gt;0 and ax+b&gt;0 OR x&lt;0 and…

Q: For what value of x does the function g(x)= -1/3x3 +2x2 convex

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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.