Frequent Limits Continuity Questions

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limx→0 sin(Ï€cos2x)/x2 ...

mathop {lim }limits_{x o 0} frac{{sin (pi {{cos }^2}x)}}{{{x^2}}} = a) - pi b) pi c) frac{pi }{2} d) 1 ...

1. lim x→0 (1+x)1/x-e+ 1/2 ex/x2 2. lim x→0( ax+bx+cx/3 )2/x ...

\lim_{x\rightarrow \infty} 100[((x+1)(x+2)...(x+100))^{1/100} - x] ...

mathop {lim }limits_{n o infty } left[ {frac{1}{n} + frac{1}{{n + 1}} + frac{1}{{n + 2}} + ....... + frac{1}{{3n}}} ight] = a) 0 b) {log _e}4 c) {log _e}3 d) {log _e}2 ...

Q1: *Image* a)-1 b)loge1 c)1 d)none q2: *Image* a) 1/2 sin3a b) 1/2 cosec2a c)sin3a d)cosec3a q3: *Image* a)1 b)-1 c)0 d)none q4:if 0<x<y then *Image* a)e b)x c)y d)none q5: *Image* a)1 b) sinx/x c) x/sinx d)none ...

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lim [(1+x)^(1/x) -e]/x x→0 ...

mathop {lim }limits_{n o infty } frac{{{1^p} + {2^p} + {3^p} + ........ + {n^p}}}{{{n^{p + 1}}}} = a) frac{1}{{p + 1}} b) frac{1}{{1 - p}} c) frac{1}{p} - frac{1}{{(p - 1)}} d) frac{1}{{p + 2}} ...

The value of a is coming as -1 and b as 1/2. But the problem is that when they are placed in the equation the result is not zero. ...

calcullate : Lt asinx-xsina /ax2-ax2x x→a. ...

if g(x)=-√(25-x2) then Lt (g(x)-g(1))/x-1 =? x→1 ...

Let and c be two vectors perpendicular to each other in the xy-plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by ...

mathop {lim }limits_{x o infty } {left[ {1 + frac{1}{{mx}}} ight]^x} equal to ...

mathop {lim }limits_{x o 0} left( {frac{{{e^x} - 1}}{x}} ight) = ...

mathop {lim }limits_{x o 0} frac{{{x^2} - 2x}}{{2sin x}} equals ...