Evaluate the following: [2.5+2.5] | Basic Mathematics 2077

Basic Mathematics20775 marksNumerical: limit evaluationLimit evaluation techniques

Evaluate the following:

$\lim_{x \to \infty} (x-\sqrt{x^2 + 16})$

$\lim_{x \to 1} \left(\frac{\sqrt{6x+10}-5}{x^2}\right)$

[2.5+2.5]

Evaluate the following:

$$\lim_{x \to \infty} (x-\sqrt{x^2 + 16})$$

$$\lim_{x \to 1} \left(\frac{\sqrt{6x+10}-5}{x^2}\right)$$

[2.5+2.5]

Limit 1: $\lim{x \to \infty} (x - \sqrt{x^2 + 16})$ - Limit 2: $\lim{x \to 1} \dfrac{\sqrt{6x+10} - 5}{x^2}$ --- Step 1: Identify the form As $x \to \infty$ , this is of the form $\infty - \infty$ (indeterminate). Step 2: Multiply by conjugate $$= \lim{x \to \infty} (x - \sqrt{x^2 + 16}) \cdot ...

Limit 1: $\lim{x \to \infty} (x - \sqrt{x^2 + 16})$ - Limit 2: $\lim{x \to 1} \dfrac{\sqrt{6x+10} - 5}{x^2}$ --- Step 1: Identify the form As $x \to \infty$, this is of the form $\infty - \infty$ (indeterminate). Step 2: Multiply by conjugate $$= \lim{x \to \infty} (x - \sqrt{x^2 + 16}) \cdot ...