Rolle Theorem f(x) = sin x + cos x. Find c ε [0,2,π]
Differentiate \(tan^{-1}(\frac{\sqrt{1+x^2}-1}{x}) \,w.r.t\,\,cos^{-1}(\frac{\sqrt(1+\sqrt{1+x^2})}{2\sqrt({i}+x^2)})\)
Mean + Variance = 1.8, n = 5, Find p(probability of success).
Find variance of first 2n natural numbers.
\( \sum (x - x_i)^2 = 100 \), no. of observations = 20, \( \sum x_i = 20 \).
Find cos248o - sin212o , if sin18o = (√5 - 1)/4
If a pair of line given by \( (x \cos \alpha + y \sin \alpha)^2 = (x^2 + y^2) \sin^2 \alpha \) are perpendicular. What is the value of α?
\( \lim_{x \to 0} \frac{x \cdot \cot(4x)}{\sin(2x) \cdot \cot^2(2x)} = ? \)
\(\int \frac{1}{\cos^3 x \sqrt{\sin 2x}} \, dx\)
\( -\tan\left(\frac{1}{x}\right) + \frac{1}{x} + c = ? \)
\(\int \frac{1}{(x + 2)(1 + x)^2} \, dx\)
The sum of mean and variance of a given set is 15/2 and their number of trials is 10, then find the value of variance?
\( \int_0^\pi \frac{x \tan(x)}{\sec(x) + \cos(x)} \, dx = ? \)
\( \int \frac{(x^2 - 1)}{x^3 \sqrt{2x^4 - 2x^2 + 1}} \, dx = ? \)
\( \int_0^1 \cos^{-1}(x) \, dx = ? \)
\( \int e^x (1 - \cot(x) + \cot^2(x)) \, dx = ? \)
Find the differential equation of all circles passing through the origin and having their centres on the x-axis.
In a certain culture of bacteria the rate of increase is proportional to the no.of bacteria present at that instant it is found that there are 10000 bacteria present in 3 hours and 40000 bacteria at the 5 hours the number of bacteria present in the beginning is?