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Mathematics
Soumil Gupta's user avatar
Soumil Gupta's user avatar
Soumil Gupta's user avatar
Soumil Gupta
  • Member for 3 years, 7 months
  • Last seen more than a month ago
  • Hyderabad, India.
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11 Answers

Score Activity Newest
3 votes

How to evaluate $\lim\limits_{x\to 0}\frac{1-\cos 7x}{3x^2}$?

3 votes

Prove that $\int_{0}^{\pi}sin^nxdx=\int_{0}^{2\pi}sin^nxdx$

3 votes
Accepted

If $f\left(0\right)=1$ and $f'\left(x\right)>3f\left(x\right)\ $ $∀\ x\ \ge0$ then prove that $f\left(x\right)\ge e^{3x}\ ∀\ x\ \ge0$

2 votes

Evaluating $\lim _{x\to \infty }\tan\left(x^2\sin\frac{\pi }{4x^2}\right)$ without L'hopital's rule

2 votes

Doubt regarding splitting of the limit $ \lim\limits_{x \to 0} \dfrac{\sin^2(3x)}{x^2} $

2 votes
Accepted

Extrema points of a non-differentiable function.

2 votes

Finding all $a$ such that $f(x)=\sin2x-8(a+1)\sin x+(4a^2+8a-14)x$ is increasing and has no critical points

1 vote

Solve : $x^6 - 12x^5 + ax^4 + bx^3 + cx^2 + dx + 64 =0$ has all positive roots then the values of $a , b , c$ and $d$ are

1 vote

Not defined in logarithmic differentiation

0 votes

If $ 3x^2 + 2\alpha xy + 2y^2 + 2ax - 4y + 1 $ can be resolved into two linear factors, then prove the following.

0 votes

Why is this calculation of $ \lim _{x \rightarrow 0}\left(\frac{1}{\sin ^{2} x}-\frac{\cos ^{2} x}{x^{2}}\right) $ wrong?