exercise-6-3-question-18-prove-that-the-function-given-by 03:33

Exercise 6.3 Question 18 prove that the function given by

Exercise 6.3 Question 18: Prove that the function given by {\displaystyle f(x) = x^3 - 3{x^2} + 3x - 100 } is increasing in R.

show-that-the-function-given-by-f-x-sin-x-is 06:37

Show that the function given by f (x) = sin x is

NCERT Exercise 6.2 Question 3: Show that the function given by {\displaystyle f(x) = \sin x } (a) increasing in {\displaystyle \left ( 0, \frac{\pi}{2} \right ) } (b) decreasing in {\displaystyle \left ( \frac{\pi}{2}, \pi \right ) } (c) neither increasing nor decreasing in {\displaystyle (0, \pi) }

find-the-integral-of-sinx-over-1-plus-sinx 08:07

Find the integral of sinx over 1 plus sinx

Question: Show that {\displaystyle \int{\frac{\sin x}{1 + \sin x}} = \sec x - \tan x + x + \text{C} }

a-ladder-5-m-long-is-leaning-against-a-wall-the-bottom-of-the-ladder-is-pulled-along-the-ground 08:58

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground

NCERT Exercise 6.1 Question 10 A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

if-x-sin-t-and-y-sin-pt-prove-that 07:01

If x sin t and y sin pt prove that

If {\displaystyle x = \sin t} and {\displaystyle y = \sin pt } , prove that {\displaystyle (1 - x^2)\frac{d^{2}y}{dx^2} - x\frac{dy}{dx} + p^2y = 0 } .

if-then-show-that-dy-over-dx-times-dx-over-dy-equals-1 07:36

If then show that dy over dx times dx over dy equals 1

If {\displaystyle a x^2 + 2hxy + b y^2 + 2gx + 2fy + c = 0 } , then show that {\displaystyle \frac{dy}{dx} . \frac{dx}{dy} = 1 } .

ncert-example-47-continuity-and-differentiability-chapter-5 04:31

NCERT Example – 47 Continuity and Differentiability Chapter 5

NCERT Example – 47 Continuity and Differentiability Chapter 5: Find {\displaystyle \frac{dy}{dx} } in the following parametric function {\displaystyle x = a^{\left ( t+\frac{1}{t} \right )}, y = {\left ( t+\frac{1}{t} \right )}^a} .

y-log-xx-sin-1xsin-x 07:23

y = (log x)^x + (sin^(-1)x)^(sin x)

Differentiate the following function w. r. t. x, Question 12: {\displaystyle y = (\log x)^x + (\sin^{-1}x)^{\sin x} }

find-the-derivative-of-the-following-function-w-r-t-x 10:07

Find the derivative of the following function w.r.t x

Question: Find the derivative of the following function w.r.t x, {\displaystyle y = \cos^{-1}\left( \frac{a + b\cos x}{b + a \cos x} \right) }

find-the-value-of-k-if-the-following-function-is-continuous 05:39

Find the value of k, if the following function is continuous

Question 8. Find the value of k, if the following function is continuous {\displaystyle f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases} }

if-x-a2-y-b2-c2-is-a-constant-independent-of-a-and-b 08:19

If (x - a)^2 + (y - b)^2 = c^2 is a constant independent of a and b.

Question 15. If { \displaystyle (x - a)^2 + (y - b)^2 = c^2 } , for some c > 0, prove that {\displaystyle \frac{\left[ 1 + \left( \frac{dy}{dx}\right )^2 \right ]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} } is a constant independent of a and b.

continuity-and-differentiability-class-12-maths-ncert-exercise-5-7-question-14 04:39

Continuity and Differentiability Class 12 Maths NCERT Exercise – 5.7 Question – 14

Question 14. If { \displaystyle y = Ae^{mx} + Be^{nx}} , show that { \displaystyle \frac{d^2{y}}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0 } .

ch05-continuity-and-differentiability-class-12-maths-ncert-exercise-5-6-question-7 17:42

Ch05. Continuity and Differentiability Class 12 Maths NCERT Exercise – 5.6 Question – 7

Question 7 : { \displaystyle x = \frac{\sin^3{t}}{\sqrt{\cos 2t}},  y = \frac{\cos^3{t}}{\sqrt{\cos 2t}} }

ncert-example-26-chapter-5-class-12-maths-find-the-derivative-of-f-given-by 04:13

NCERT Example 26 Chapter 5 Class 12 Maths Find the derivative of f given by

Example 26 Find the derivative of f given by { \displaystyle f(x) = \sin^{–1} x } assuming it exists.

find-the-value-of-a-if-the-following-function-is-continuous 05:21

Find the value of a, if the following function is continuous

Find the value of a, if the following function is continuous
Question 17: {\displaystyle f(x) = \begin{cases} a \sin \frac{\pi }{2} (x+1), & \text{ if } x \le 0 \\ \frac{\tan x-\sin x}{x^{3} }, & \text{ if } x > 0 \end{cases}}

given-a-square-matrix-of-order-3x3-such-that-a-12-find-the-value-of-%e2%88%a3a-adja%e2%88%a3 02:03

Given a square matrix of order 3×3 such that | A | = 12 find the value of ∣A adj(A)∣

Question: Given a square matrix of order 3×3 such that | A | = 12 find the value of ∣A adj(A)∣

express-the-following-matrices-as-the-sum-of-symmetric-and-a-skew-symmetric-matrix 06:04

Express the following matrices as the sum of symmetric and a skew symmetric matrix

Question 4. Express the following matrices as the sum of symmetric and a skew symmetric matrix: {\displaystyle {\begin{bmatrix} 2&{ - 2}&{ - 4}\\ { - 1}&3&4\\ 1&{ - 2}&{ - 3} \end{bmatrix}} }

show-that-the-matrix-b%e2%80%b2ab-is-symmetric-or-skew-symmetric-according 06:01

Show that the matrix B′AB is symmetric or skew symmetric according

NCERT Miscellaneous Exercise Question 5 : Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

there-are-two-families-a-and-b-there-are-4-men-2-women-and-1-child-in-family-a 11:52

There are two families A and B. There are 4 men, 2 women and 1 child in family A

There are two families A and B. There are 4 men, 2 women and 1 child in family A and 2 men, 3 women and 2 children in family B. They recommended daily allowance for calories i.e. Men: 2000, Women: 1500, Children: 1200 and for proteins is Men: 50 gms., Women: 45 , Children: 30 gms. Represent the above information by matrices, using matrix multiplication calculate the total requirements of calories and proteins for each of the families.

show-that-ab-is-a-zero-matrix-provided-%ce%b8-%e2%88%92-%cf%95-is-an-odd-multiple-of-%cf%80-over-2 11:22

Show that AB is a zero matrix, provided θ − ϕ is an odd multiple of π over 2

Question 7. If {\displaystyle A = { \begin{bmatrix} {\cos^2\theta} & {\cos \theta \sin \theta} \\ {\cos \theta \sin \theta } & {\sin^2 \theta} \end{bmatrix} } } , {\displaystyle B = {\begin{bmatrix} {\cos^2 \phi} & { \cos \phi \sin \phi } \\ {\cos \phi \sin \phi } & {\sin^2 \phi } \end{bmatrix}} } then show that AB is a zero matrix, provided {\displaystyle (\theta  - \phi )} is an odd multiple of {\displaystyle \frac{\pi }{2}} .

simplify-sin-inverse-5-over-13-cos-x-plus-12-over-13-sin-x-rd-sharma-question 06:15

Simplify sin inverse 5 over 13 cos x plus 12 over 13 sin x RD Sharma Question

Simplify: {\displaystyle \sin ^{-1} \left ( \frac{5}{13} \cos x+\frac{12}{13} \sin x \right ) }

ncert-exercise-2-2-question-9-inverse-trigonometric-functions 07:19

NCERT Exercise 2.2 Question 9 Inverse Trigonometric Functions

NCERT Exercise 2.2 Question 9 Inverse Trigonometric Functions { \displaystyle {\tan }^{-1} \left ( \frac{x}{\sqrt{a^2-x^2}} \right ), | x | < a}

check-if-a-function-is-one-one-and-onto 09:10

Check if a function is one-one and onto

Question. Let A = R – {3} and B = R – {1}. Consider the function {\displaystyle f: A \rightarrow B } defined by {\displaystyle f(x) = \frac{x-2}{x-3} } . Is f one-one and onto? Justify your answer.

equivalence-relations-and-equivalence-classes 06:11

Equivalence Relations and Equivalence Classes

A relation R on set A is said to be reflexive if (a, a) ∈ R, ∀ a ∈ A or aRa,∀a ∈ A symmetric if(a, b) ∈ R ⇒ (b, a) ∈ R, ∀ a, b ∈ A or aRb ⇒ bRa,∀ a, b ∈ A transitive if (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R, ∀ a, b, c ∈ A or aRb and bRc ⇒ aRc ,  ∀ a, b, c ∈ A If a relation is reflexive, symmetric and transitive then the relation is said to be equivalence relation.