List of top Mathematics Questions on Calculus

The differential equation of all non vertical lines in a plane is:
Negation of the statement \( (\rho \land r) \rightarrow (r \lor q) \) is
Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]
Find the limit \[ \lim_{x \to 0} \left( 1 + \tan^2 \sqrt{x} \right)^{3/x} \]
Find the area of the figure bounded by the parabola \( y^2 = 4x \) and \( x^2 = 4y \).
The value of \( \int_0^{\frac{\pi}{2}} e^x \cos x \, dx \) is equal to:
Choose the most appropriate options. Let \( P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} \) and \( Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} \). Then,
The series \( 1 + 1 + \frac{3}{2^2} + \frac{4}{2^3} + \frac{5}{2^4} + \cdots \) is equal to
The value of the integral \( \int_{-3}^{5} |x - 3| \, dx \) is
Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]
The value of \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (x^2 \sin x + x^3) \, dx\) is:
Solution of the differential equation\( \frac{dy}{dx}=y^2\) with the condition y(1)=1 is