_ x 0 y^2 x = ........, where y^2 = ax + b x^2 + c x^3 - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{{{y^2}}}{x} = ........$, where ${y^2} = ax + b{x^2} + c{x^3}$

A
$0$
B
$1$
✓
$a$
D
None of these

✓

Answer

Correct option: C.

$a$

c
(c) $\mathop {\lim }\limits_{x \to 0} \,\frac{{ax + b{x^2} + c{x^3}}}{x} = \mathop {\lim }\limits_{x \to 0} \,\frac{{a + bx + c{x^2}}}{1} = a.$

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 "MCQ" from 12. limits→12. limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Poonam buys a fish from a shop for her aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?

For $x \in R$, let $[x]$ denote the greatest integer $ \le x$, then the sum of the series $\left[ { - \frac{1}{3}} \right] + \left[ { - \frac{1}{3} - \frac{1}{{100}}} \right] + \left[ { - \frac{1}{3} - \frac{2}{{100}}} \right] + .....+\left[ { - \frac{1}{3} - \frac{{99}}{{100}}} \right]$

A straight line makes an angle of ${135^o}$ with $x$-axis and cuts $y$-axis at a distance of -$5$ from the origin. The equation of the line is

The normal at a point $P$ on the ellipse $x^2+4 y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid point of the line segment $P Q$, then the locus of $M$ intersects the latus rectums of the given ellipse at the points

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is:

Complete 2, 4, 6, 8, ____________.

The length of the latus-rectum of the parabola $x^2-4 x-8 y+12=0$ is

$0.14189189189….$ can be expressed as a rational number

A number is chosen at random from the set $\{1,2,3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500\ p$ is. . . . . .

Let $S=\left\{z \in C : z^{2}+\bar{z}=0\right\}$. Then $\sum \limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))$ is equal to$......$