Evaluate the following limit: _ x - ( 4x^2-7x +2x ) - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-\infty}\big(\sqrt{4\text{x}^2-7\text{x}}+2\text{x}\big)$

✓

Answer

$\lim\limits_{\text{x}\rightarrow-\infty}\big(\sqrt{4\text{x}^2-7\text{x}}+2\text{x}\big)$
Substitute y = -x
$=\lim\limits_{\text{y}\rightarrow\infty}\Big(\sqrt{4\text{y}^2+7\text{y}}-2\text{y}\Big)$
$=\lim\limits_{\text{y}\rightarrow\infty}\frac{\Big(\sqrt{4\text{y}^2+7\text{y}}-2\text{y}\Big)\Big(\sqrt{4\text{y}^2+7\text{y}}+2\text{y}\Big)}{\sqrt{4\text{y}^2+7\text{y}}+2\text{y}}$
$=\lim\limits_{\text{y}\rightarrow\infty}\frac{\Big(4\text{y}^2+7\text{y}+4\text{y}^2\big)}{\sqrt{4\text{y}^2+7\text{y}}+2\text{y}}$
$=\lim\limits_{\text{y}\rightarrow\infty}\frac{(7\text{y})}{\sqrt{4\text{y}^2+7\text{y}}+2\text{y}}$
$=\lim\limits_{\text{y}\rightarrow\infty}\frac{7}{\sqrt{4+\frac{7}{\text{y}}}+2}$
$=\frac{7}{2+2}=\frac{7}{4}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(4 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

How many numbers between 100 and 1000 have the digit 7 exactly once?

Differentiate the following from the first principle$\sqrt{\sin(\text{3x}+1)}$

Show that the line $8 y+x=17$ touches the ellipse $x^2+4 y^2=17$. Find the point of contact.

Evaluate the following limit:
Evaluate: $\lim\limits_{\text{n}\rightarrow\infty}\frac{1.2+2.3+3.4+\ \cdots+\text{n}(\text{n}+1)}{\text{n}^3}$

Find the number of ways of selection 9 balls from 6 red balls, 5 white balls and 5 balls if each selection consists of 3 balls of each colour.

Prove by the method of induction, for all n ∈ N.

$\left(2^{3 n}-1\right)$ is divisible by 7 .

The odds against a husband who is 60 years old, living till he is 85 are 7 : 5. The odds against his wife who is now 56, living till she is 81 are 5 : 3. Find the probability that : (i) at least one of them will be alive 25 years hence. (ii)exactly one of them will be alive 25 years hence.

A box contains three coins: two fair coins and one fake two-headed coin. A coin is picked randomly from the box and tossed.(i) What is the probability that it lands head up?(ii) If happens to be head, what is the probability that it is the two-headed coin?

Prove that:
$4\cos\text{x}\cos\Big(\frac{\pi}{3}+\text{x}\Big)\cos\Big({\frac{\pi}{3}-\text{x}}\Big)=\cos3\text{x}$

If $\sin(\alpha+\beta)=1$ and $\sin(\alpha-\beta)=\frac{1}{2}$ where $0\leq\alpha,\beta\leq\frac{\pi}{2}$ than find the values of $\tan(\alpha+2\beta)$and $\tan(2\alpha+\beta).$