Recently Active Mathematics Questions

Saw this recently " A root of an equation f(x)=0 is said to have a multiplicity k if its k times repeated root " eg. (x-1)2=0 has x=1 as a root of multiplicity 2 (x-1)2(x-2)3=0 has x=1 as a root of multiplicity2 and x=2 as a ...

A biologist watches a chameleon. The chameleon catches flies and rests after each catch. The biologist notices that: (i) The first fly is caught after a resting period of 1 minute. (ii) The resting period before the 2mth fly ...

if xp yq = ( x+y )p+q then find dy/dx ...

if xp yq = ( x+y )p+q then find dy/dx ...

wat is simpsons rule...? ...

let 'f' be a twice differntiaible function such that f''(x)= - f(x) and f'(x)= g(x) for all x ε R. If h'(x)=[ f(x)]2 +[ g(x) ]2 , h(1)= 8; h(0) =2 then h(8) = a. 16 b. 32 c. 40 d. 50 ...

If a fn. satisfies f(x+1)+f(x-1)= 2 f(x) then find the period of f(x). ...

let g(x) be a continous function for all x ,and f(x) = f(a) +(x-a)g(x) for all x ε R , then a. f(x) is necessarily differentiable at x =a b. f(x) is not necessarily differentiable at x=a c. f(x) is not necessarily continous ...

f(x)= Sin-1(Cos-1[x]) ...

f(x)= (2x4 - 14x2 - 8x +49)/(x4-7x2-4x+23) ...

can someone plz tell me how to do these types: 1. is the function f:R→R 3x(x-3) invertible?? if not change its domain so that it becomes so. 2.let g(x)=x2-4x-5 a) g is one-one on R b)g is one-one on (-∞,2] c)g is not one- ...

The eqn-- ex-ax-b=0 has A. 1 real root if a<0 B. 1 real root if b>0 & a<=0 C. 2 real roots if a>0 & a.ln a>=(a-b) D. No real root if a ln a<a-b Multiple Ans correct ...

let Pn = aPn-1 -1 for all n= 2,3,4,.. and let P1= ax-1 where a ε R+ then evaluate the limit lim ( x → 0 ) Pn/x ...

prove that \frac{1}{15}<\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}........\frac{99}{100}<\frac{1}{10} ...

here's a nice one i came across while reading a book yesterday prove for all positive integers m, the integer next greater than (\sqrt{3}+1)^{2m} contains 2^{m+1} as a factor ...

an 8 x 8 array consists of the numbers 1,2,3,.............,64 . consecutive numbers are adjacent along a row or coloumn. what is the minimum value of sum of numbers along a diagonal ? ...

Matrix ! If A = [ 0 2 ] , kA = [0 3a ] whatz value of k , a & b 3 -4 2b 24 please show how ! thanks ...

if y=sin-1(cos x) , then dy/dx=? a)sin2x b) sinx c)-1 d)none ...

1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...

what is the coefficient of x99 in (x-1)(x-2)(x-3)......(x-100) is 1. -5050 2. 5050 ...

29. The number of permutations of the word HINDUSTAN such that none of the three patterns HIN, DUS, TAN occurs is (1) 169194 (2) 166680 (3) 169190 (4) 166670 ...

LCM of two fractions -- a1/b1 & a2/b2 is = LCM(a1,a2) / HCF(b1.b2) . Prove ...

find the fifth derivative of y= 1/(1+x2) please give a good method ...not the tedious one !! ...

solve sin^{7}x +cos^{7}x=1 ...

∫(x3m+x2m+xm)(2x2m+3xm+6)1/mdx note: do without using integration by parts ...

hi! i am new to this topic , so pls help ∫(x2tan-1x3)dx/(1 + x6) note: do without using integration by parts ...

(12x-1)(6x-1)(4x-1)(3x-1)=5 SOLVE ...

The value of scalar triple product remains the same so long as the cyclic order of the vectors a,b,c is maintained i.e [abc]=[bca]=[cab] [abc]=-[bac] Can someone pls explain wat is meant by cyclic order? ...

1! + 2! + 3! ............. + n! = k! where kεI+ find all solutions ...

Find all polynomial P(x) with real coefficients satisfying P^2(x)+P^2(x-1)=2(P(x)-x)^2 ...