Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY5 Marks
Question
If y = $\frac{\sin^{-1}\text{x}}{\sqrt{\text{1 - x}^{2}}}$ show that
$(1-\text{x}^{2})\frac{\text{d}^{2}\text{y}}{\text{dx}}-\text{3x}\frac{\text{dy}}{\text{dx}}-\text{y}=0.$
✓

Answer

$\sqrt{\text{1 - x}^{2}}\text{ y}=\sin^{-1}\text{x}$
$\sqrt{\text{1 - x}^{2}}\text{ }\frac{\text{dy}}{\text{dx}}-\frac{\text{xy}}{\sqrt{\text{1 - x}^{2}}}=\frac{1}{\sqrt{\text{1 - x}^{2}}}$
$\Rightarrow\text{(1 - x)}^{2}\text{ }\frac{\text{dy}}{\text{dx}}-\text{xy}=1$
$\Rightarrow\text{(1 - x)}^{2}\text{ }\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{ 2x }\frac{\text{dy}}{\text{dx}}-\text{ x }\frac{\text{dy}}{\text{dx}}-\text{y}=0$
$\Rightarrow\text{(1 - x)}^{2}\text{ }\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{ 3x }\frac{\text{dy}}{\text{dx}}-\text{ y }=0.$

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 "5 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int\frac{\text{x}^2}{\sqrt{3\text{x}-4}}\text{dx}$
→
Find the angles of a triangle whose vertices are A (0, -1 ,-2), B(3, 1 ,4) and C(5 ,7 ,1).
→
If $\vec{\text{a}} , \vec{\text{b}} , \vec{\text{c}}$ are mutually perpendicular vectors of equal magnitudes, show that the vector $\vec{\text{a}} + \vec{\text{b}} + \vec{\text{c}}$ is equally inclined to $\vec{\text{a}} , \vec{\text{b}}$ and $\vec{\text{c}}$ Also, find the angle which $\vec{\text{a}} + \vec{\text{b}} + \vec{\text{c}}$ makes with $\vec{\text{a}} \text{ or }\vec{\text{b}} \text{ or } \vec{\text{c}}.$
→
Prove that the semi $-$ vertical angle of the right circular cone of given volume and least curved surface area is $\cot ^{-1} \sqrt{2}$
→
Show that the line whose vector equation is $\vec{\text{r}}=2\hat{\text{i}}+5\hat{\text{j}}+7\hat{\text{k}}+\lambda(\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}})$ is parallel to the plane whose vector equation is $\vec{\text{r}}\cdot(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}})=7$ Also, find the distance between thetm.
→
Evaluate the following integrals:
$\int\limits^{\pi}_0\text{x}\cos^2\text{x dx}$
→
Without expanding, show that the values of the following determinant are zero:
$\begin{vmatrix}1&43&6\\7&35&4\\3&17&2\end{vmatrix}$
→
If $\text{y}=\cot^{-1}\Big\{\frac{\sqrt{1+\sin\text{x}}+\sqrt{1-\sin\text{x}}}{\sqrt{1+\sin\text{x}}-\sqrt{1-\sin\theta}}\Big\},$ show that $\frac{\text{dy}}{\text{dx}}$ is independent of x.
→
A firm manufactures two types of products $A$ and $B$ and sells them at a profit of Rs $2$ on type $A$ and Rs $3$ on type $B.$ Each product is processed on two machines $M_1$ and $M_2.$ Type A requires one minute of processing time on $M_1$ and two minutes of $M_2;$ type $B$ requires one minute on $M_1$ and one minute on $M_2$. The machine $M_1$ is available for not more than $6$ hours $40$ minutes while machine $M_2$ is available for $10$ hours during any working day. Formulate the problem as a LPP.
→
A manufacturer has employed 5 skilled men and 10 semi-skilled men and makes two models A and B of an article. The making of one item of model A requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. One item of model B requires 1 hour by a skilled man and 3 hours by a semi-skilled man. No man is expected to work more than 8 hours per day. The manufacturer’s profit on an item of model A is Rs. 15 and on an item of model B is Rs. 10. How many of items of each model should be made per day in order to maximize daily profit? Formulate the above LPP and solve it graphically and find the maximum profit.
→