8. Give an e-8 proof of the following statement: VaeR, lim f(x) does not exist where f(x) = { (0 ifx is rational 1 ifx is irrational

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

Q: 15. Vlad and Karl discuss about the continuity of the given function. Vlad asserts that the function…

A: A function f(x) is said to be continuous at x=a iff limx→a-f(x)=limx→a+f(x)=f(a) A polynomial…

Q: If f(x) = lim (1+x)(1+x²) (1 + x² ) (1 + x² ).......((1+x) where [x] < 1, then - 618 1 (B) 3) (C)…

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Q: 2. Discuss the continuity of f(x) by answering the following questions. т - 5, for z 3. f(x) = for –…

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Q: 10. Find the value(s) of c so the following function is continuous for all real numbers. f(x) = { =…

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Q: Translate the statement lim f(x) 5 in terms of a rigorous e and N state-

A: Solution Given limx→∞f(x)=5we need to translate the statement in term of a rigorous ∈ and N…

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: Vx-2 11. lim- x→4 4-x 1 12. lim 1 3 13. lim x-→2-x-2 x² –4 x-1 14. lim |2x – x² –1

A: According to bartleby rule I answered first 4 questions

Q: Use the convergence theorem to determine the sum of the Fourier series of the function on the…

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

Q: 7. Prove by definition that limx→1 x³ = 1. [Hint: x³ - 1 = (x − 1)(x² + x + 1).]

A:

Q: x* - 1 7. lim X-1+ x - 1 - 1

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Q: 5. Find values for a and b that will make f continuous everywhere, if: f(x) = Show your work. { 2x +…

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Q: 6. Suppose f and g are functions with domain R. If bothf and g are even but f+g is odd, then prove…

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Q: 6. Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove…

A: A function defined on a domain R is said to be even if , f(-x)=f(x) ∀x∈R A function defined on  a…

Q: 7. Show that lim x³ = c³ for any c E R. X-C

A: To prove:- for any

Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

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Q: |2а — 10| limr→0- -1 x-5 O True False

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Q: Q.1: Evaluate Vx+25 -5 х2-10х (1) lim (2) lim x-12 Vx+4 x (х+3) 2x2+3 x2-25 (3) lim (4) lim X-5 x-5…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: x +1 f(2 – 3h) – f(2) If f(x) = what is lim h→0 5 С. 16 ? x +2 h 3 А. 16 -5 D. 16 3 3 Е. 13 В. - 16

A: Given the function f(x)=x+1x+2

Q: . Let f RR be defined by setting f(x) = x if x is rational and f(x) = 0 if x is irrational. Use the…

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Q: lim (x, y) (1,2) 6x² + 3x²y–3xy² 4x-y 9 O a. 4 O b. 3 3 O d. 3 e. does not exist 3/4 4/9 4/3 /172

A: We have to solve

Q: Find lim (₁x) (0,0) (x²-16) (0₁ [(x-4)² ty ²] if it exists

A: Let,the given limit is

Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

A: