Recently Active Calculus Questions

xlog_e(\frac{x^y}{e^x})\frac {dy}{dx}=ylog_e(\frac {y^x}{e^y}) ...

∫-∞∞ (sint/t) dt ...

1) if f(2x + y/8 ,2x - y/8 )=xy then f(x,y) +f(y,x)=??? 2)the function f(x)=λmod(sinx) + λ2mod(cosx) +g(λ) has a period equalt to pie/2 then find λ 3)evaluate the limit \lim_{x\rightarrow \infty }(\frac{x}{2}cos(\frac{\pi ...

Q1. \lim_{n\rightarrow \infty }\sum_{k=0}^{n}{\frac{^nC_{k}}{n^k(k+3)}} Q2. If the roots of the equation ax2+bx+c=0, a>0 are positive and are p and q (p>q) then \lim_{x\rightarrow 1/p^+}\sqrt{\frac{1-cos[2(cx^2+bx+c)]}{ ...

If ax2 - bx + c = 0 have two distinct roots lying in the interval (0,1), a, b, c ε N, then prove that log5(abc) ≥ 2. ...

lxl= 1-t2/1+t2 y= 2t/1+t2 tε[-1,1] ...

COMPREHENSION let f(x) and g(x) are two distinct functions such that f(x) is an odd function and g(x) is an even function for all X ε R . Let a function h(x)=f(x) +g(x) is an odd function and φ(x)=f(g(x))+g(f(x)). NOW ANSWE ...

plz solve this one : [1] *Image* q2 try this one also its not my doubt but wanted to share if log(\frac{1}{1+x+x^2 +x^3 }) is expanded on the ascendind powers of x then prove that coefficient of xn in the expansion is \frac{- ...

find the value of x satisfying \int_{0}^{2[x+14]}{\left\{\frac{x}{2} \right\}}dx=\int_{0}^{\left\{x \right\}}{\left[x+14 \right]}dx wer [.] is gif and { } fractional part of x this is an easy one but my ans not matching[2] ...

1) Find \lim_{x\rightarrow0}{{\left( \frac{1^{x}+2^{x}+3^{x}+.....+n^{x}}{n}\right)^{1/x}}} 2) Find \lim_{n\rightarrow(infinity)}\frac{1^{k}+2^{k}+3^{k}+........+n^{k}}{n^{k+1}} ...

p *Image* ...

Q. If m=np and p+q=1, then \lim_{n\rightarrow \infty } \; ^{n}C_{r}q^{n-r}p^{r} is equal to (a) e-mmr/r! (b) e-m(m/1)*(m/2)*...(m/r)*(1/r+1) (c) (m/1)(m/2)...(m/r)(1/em) (d) e-mmr/(r+1)! ...

find the values of a for which the equation- (x-1)2=|x-a| has exactly 3 solutions ...

Q1. Let f(x+y) = f(x).f(y) for all x,y belongs to R and f(5) = 2 and f'(0) = 3. Then f'(5) = ? Q2. Let f(x) be defined in R such that f(1) = 2 and f(2) = 8 and f(u+v) = f(u) + kuv - 2v2 for all u,v belongs to R and k is a fix ...

Q1...................... for 0< \theta <\pi /2 the solutions of \sum_{m=1}^{6}{cosec(\theta +\frac{(m-1)\pi }{4}}).cosec(\theta +\frac{m\pi }{4})=4\sqrt{2} are 1) pi/4 2)pi/6 3)pi/12 4)5pi/12 P.S i want a shorter method ...

Area bounded by the curve y=ex2, x-axis and the lines x=1, x=2 is given to be equal to a sq units. Area bounded by the curve y=√(ln x) , y-axius, and the lines y=e and y=e4 is equal to ? ...

sir please give steps on calculating the period of a function, ...

Let g be a continuous function and attains only rational values. If g(0) = 5, then the roots of the equation (g(2009))x2 + (g(2008))x + (g(2010)) = 0 are 1. Real and equal 2. Real and unequal 3. Rational 4. Imaginary ...

evalute this limit \lim_{x\rightarrow \infty }x^{3}\left\{\sqrt{x^{2}+\sqrt{1+x^{4}}}-x\sqrt{2} \right\} ...

1)...... let A0 denotes the area bounded by f_{n}(x)=\left|\frac{sin(8nx)+cos(8nx)}{x} \right| , x -axis,y-axis and the line x=\pi /8 the prove that A_{n}>\frac{2\sqrt{2}}{\pi }\left[1+\frac{1}{2}.......\frac{1}{n} \right] ...

f:R\rightarrow R satisfies the following relation: f(x+1)f(x)+f(x+1)+1=0 prove that f is not continuous. ...

\sum_{n=0}^{\ \propto }{1/(3n+1)-1/(3n+2)} ...

Q1 \int_{0}^{[x]/3}{\frac{8^x}{2^{[3x]}}}dx where [.] is gint Q2 k ε N and I_k=\int_{-2k\pi}^{2k\pi}{\left|\sin x \right|}[\sin x]dx find \sum_{k=1}^{100}I_k Q3 I=\int_{sin^{-1}\alpha}^{cos^{-1}\alpha}{\frac {sinx}{sinx+cosx ...

Here β represents beta function Q1 If \int_{0}^{n}{(1-\frac{x}{n})^n}x^{k-1}dx=R.\beta (k,n+1) find R Q2 If \int_{0}^{\infty}{\frac{x^{m-1}}{(1+x)^{m+n}}}dx=k.\int_{0}^{\infty}{\frac{x^{n-1}}{(1+x)^{m+n}}}dx ,find value of k ...

prove that : (3+ 3 ) + (3- 3 ) <2 3 ...

f(x) = x3 + x2 + kx + 4 is increasing function and the least positive integral value of k is P1. If the angle between y=\left[\sqrt{1-sin^2x}+\sqrt{1-cos^2x} \right] (where [] represents greatest integer function ) and X- axi ...

1> lim n→∞ ( xn/n!) 2> lim n→∞ n2(x1/n - x1/(n+1)) also say the method ...

FIND THE VALUE OF THE LIMIT AND SAY THE PROCEDURE lim n→∞ 1/2 tan(x/2)+1/22 tan(x/22)+1/23 tan(x/23).........+1/2n tan(x/2n) ...

Lim x→0 (1/x2) - cotx ...

FIND THE VALUE OF THE LIMIT AND SAY THE PROCEDURE lim n→∞ 1/2 tan(x/2)+1/22 tan(x/22)+1/23 tan(x/23).........+1/2n tan(x/2n) ...