Question

Exercise 4.2.5. Use Definition 4.2.1 to supply a proof for the following limit statements. (a) $\lim_{x \to 2} (3x + 4) = 10$. (b) $\lim_{x \to 0} x^3 = 0$. (c) $\lim_{x \to 2} (x^2 + x - 1) = 5$. (d) $\lim_{x \to 3} \frac{1}{x} = \frac{1}{3}$.

          Exercise 4.2.5. Use Definition 4.2.1 to supply a proof for the following limit statements.
(a) $\lim_{x \to 2} (3x + 4) = 10$.
(b) $\lim_{x \to 0} x^3 = 0$.
(c) $\lim_{x \to 2} (x^2 + x - 1) = 5$.
(d) $\lim_{x \to 3} \frac{1}{x} = \frac{1}{3}$.

Exercise 4.2.5. Use Definition 4.2.1 to supply a proof for the following limit statements.
(a) limx → 2 (3x + 4) = 10.
(b) limx → 0 x^3 = 0.
(c) limx → 2 (x^2 + x - 1) = 5.
(d) limx → 3(1)/(x) = (1)/(3).

Added by Sean H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Naresh Bagrecha

Step 1

Let's start by manipulating the expression |(-2x+4) - 10| < ε: |-2x+4 - 10| < ε |-2x - 6| < ε |2(x + 3)| < ε 2|x + 3| < ε Now, we can see that if we choose δ = ε/2, then for any 0 < |x - a| < δ, we have: |2(x + 3)| < 2δ = 2(ε/2) = ε Show more…

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Text: Advanced Calculus Exercise 4.2.5. Use Definition 4.2.1 to supply a proof for the following limit statements: a) lim(âˆ’2x+4)=10. b) lim(x^3)=0. c) lim(2x+x^2)=5. d) lim(11)=?