1. Examine the continuity of the fiunctions given below: (a) f(x) =x -5atx 2 (b) f(x)= 2x +7atx 0 (c) f(x) =x +7atx 3 (d) f(x) =px +qatx =-4 2. Show that f (x)-2a+3b is continuous, where a and b are constants 3. Show that 5 x+7 is a continuous finction

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Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

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Q: 1. Test the continuity of the following functions at given points? x² -1 -1 <x<0 2x 0 <x<1 (a) fx)=…

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Q: 1- Discuss the continuity of the following functions at given points { V9r4+x² 5x2+3x+1 ,if a 0 (a)…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: 2. Find the linearization L(x) of f(x) = x³ - 2x + 3 at x = 2 and use it to approximate f(1.9) and…

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Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

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Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

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Q: Let f(r) = 1-5r2. Use the limit definition of the derivative to show that f'(z) = -10r. %3D

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Q: b. Test the continuity of the following function 1, V1-x,0sIs1, at x = 0,1 (x-2, x<0 x21

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Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: Determine whether the function 2х + 1 f(x) %3D 2r2 2x2 – x – 1 is continuous: a. at 2; b. at 1.

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Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: 1. Test the continuity of the following functions at given points? -1 -1 Sx <0 2x (a) fx)= X = 1…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: Use the comparison theorem with f(x) = = 1 √x r∞ 1 •√₂ √I-1 to show that is divergent.

A: Solution is given below:

Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: Suppose that f(1) = -3, f(4) = -4, f'(1) = -3, f'(4) = -5, and f" is continuous. Find the value of…

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Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

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Q: Suppose that  f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 5, and f ''  is continuous. Find the value of…

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Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

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Q: Compute the linearisation l(x) of f(x) = √1+x3 at x=2 and use this to estimate f(2.05)

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Q: Q4: Discuss the continuity of : 1 for x2

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Q: Find the values of a and b such that the following function f(x) = 2a cos(x + 1) - b.5x+2, if x -1,

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Q: 5. Find the linearization L(x) of f at a = 0 f(x) = = 1 = 0 2+x

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Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

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Q: Prove: f(x)=5x y is continuous at x=2

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A: Given: f(x,y,z)=1x2+y2+z2-1.

Q: 6. Discuss the continuity for the following functions x+y a) f(x,y) = 4x2-y2-4 x+y b) f(x, y) = %3D…

A: The objective is to discuss the continuity of the functions.

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

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