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Lalit Tolani
  • Member for 1 year, 4 months
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11 votes

If $x^{19}+x^{17}+x^{13}+x^{11}+x^{7}+x^{5}+x^{3}$ is divided by $(x^2 +1)$, then find the remainder

10 votes
Accepted

Evaluating $\sum_{r=1}^{89} \frac{1}{1+\tan^3 r}$

10 votes

Evaluating the Integral $\int_{0}^{\infty} \frac{x^{49}}{(1+x)^{51}} dx$

10 votes
Accepted

What happens to $w=\frac{x^2y^3}{z^4}$ , if $x,y,z$ increase by $\%1$ , $\%2$ , $\%3$ respectively?

7 votes

graph $x=\cos 2t, y=4 \sin t$

5 votes
Accepted

Finding the discriminant of a quadratic equation from the given information on the roots of a quadratic equation

5 votes
Accepted

Is there some reason why $\ln(x^2+x) - \ln x = \ln (x+1)$ would not always be true?

5 votes
Accepted

Using first principles find derivative of ln(sec(x))

4 votes
Accepted

Simplify $\sum_{m=1}^{6} \frac{1}{(\sin k)(\sin k - \cos k)}$ where $k = \theta + \frac{m \pi}{4}$

4 votes

Differential equation involving Newton's law of gravitation

4 votes
Accepted

If $\log_2\sin(10^{\circ})=\alpha$, what is the value of $\log_2\left(\dfrac{\sin20^{\circ}+\sin40^{\circ}}{\sin20^\circ}\right)$?

4 votes
Accepted

Why is $ 2 \cos(\frac{2π}{5}) + \left(2 \cos(\frac{2π}{5})\right)^2 = 1$?

4 votes
Accepted

Find the limit of $(1+\frac{1}{n^2})(1+\frac{2}{n^2})...(1+\frac{n}{n^2})$.

4 votes

Need help graphing an absolute value function

4 votes
Accepted

Trying to evaluate : $\int \frac{e^{x^2}+2xe^{x}}{e^{x^2}+e^x} dx$

3 votes

Is one of the roots of a linear equation $\infty$?

3 votes
Accepted

Understanding why $\log_2 (3) > 0$.

3 votes

Suppose $2+7i$ is a solution of $2z^2+Az+B=0$, where $A,B \in \mathbb{R}$ . Find $A$ and $B$

3 votes
Accepted

Relating two definite integrals

3 votes

Prove $\frac{1}{2}-\frac{4}{\pi^2}=\frac{\pi^2}{2^2\cdot4!}-\frac{\pi^4}{2^4\cdot6!}+\frac{\pi^6}{2^6\cdot8!}-\frac{\pi^8}{2^8\cdot10!}+\dots$

3 votes

Range of a rational algebraic function

3 votes
Accepted

Solve the equation: $ 3^{2x+1}+4 \cdot 3^x = 15 $

3 votes

Can you transform the denominator of each term in an infinite series?

2 votes

Calculate the general solution and the specific solution of the following differential equation: $(3y - 1)^2) (y'^2) = 4y$

2 votes

Prove $\left(\frac{u}{a}\right)^a.\left(\frac{v}{b}\right)^b.\left(\frac{w}{c}\right)^c \le \left(\frac{u+v+w}{a+b+c}\right)^{(a+b+c)} $

2 votes
Accepted

Value of $\sum_{n=0}^{1947}\frac{1}{2^n+\sqrt{2^{1947}}}$ $?$

2 votes

Notation for difference of sums with different indicies

2 votes

$x_1$ , $x_2$ are roots of $x=5-x^2$. Find the equation with roots $\frac1{(x_1+1)^3}$ and $\frac1{(x_2+1)^3}$.

2 votes

Find an arithmetic progression for which $\begin{cases}S_n-a_1=48\\S_n-a_n=36\\S_n-a_1-a_2-a_{n-1}-a_n=21\end{cases}$

2 votes
Accepted

How does $\log_2 \epsilon^{-n}$ become $n\log_2(1/\epsilon)$?