Prove using the e-8 notation that the following functions are continuous at p= 1: (a) g2(r) = 2=+7 2+7 %3D (b) g2(x) = %3D I+7

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Suppose that a continuous function g satisfies: | 9(2)de = 12 and | 9(20)da = 24. Find og(3x²)dx.

A: Given that, ∫03gxdx=12, ∫06g2xdx=24 Let  ∫06g2xdx=24 Apply the substitution u = 2x to find this…

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Develop a first-order method for approximating f" (x) which uses the data f (x – 5h), f (x – 3h), f…

A: We have to develop a first-order method for approximating f''(x) which uses the data f(x-5h),…

Q: Cx² f(x) = = if x 1 { 6 C-X

A:

Q: The range of the function f (x) = 2+ V9 – x² is [2, 5] O [0,3] О -3, 3] O [-1,2] O [-3,0]

A: Explanation of the answer is as follows

Q: Let f: R - R and g: R - R be functions given by f(x) x' and g(x) x + 5. Find g of and fog

A: Answer

Q: Let 1 f(x) = x + 15 f (2) = Submit Question

A:

Q: Which of the following functions has a removable discontinuity at x = 1? X-1 A g(x) =. x2 x2 g(x) =…

A: In a rational function, if the numerator is factorable and then the denominator cancels, then the…

Q: -kx + 1, x>4 a) Find the value k, if the function f (x) = (x² – 3x + 1, x 4

A: Given, fx = x2-3x+1,    x≤4-kx+1,         x &gt;4   We have to find the value of k for which the…

Q: Let g be the function given by g(x) = C (2 – 5t – 14) dt. What is the x-coordinate of the point of…

A:

Q: Sketch the graph of f

A: To sketchf(x)=ln|x-1|

Q: Let f(x) = a2 +1, g(æ) = Va+3, h(x) = 4 (go(hof))+(gof) at x=2? %3D Find I-4

A:

Q: Decompose the following functions (write them as compositions): (a) If h(x) = V13² + 3, what are two…

A:

Q: Use Runga-Kutta 4 to determine y(1.3) for f(r, y) = with y(1)%3D 1

A: Here we have to use Runga Kutta 4 method

Q: Evaluate f(x – 1)Vxª – 4x – 2dæ -

A: Given:      ∫x3-1x4-4x-23dx      =∫x3-1x4-4x-213dx   substitute u=x4-4x-2…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.