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41 Cards in this Set
- Front
- Back
- 3rd side (hint)
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lim(x➡infinity)[1+1/x]^x ; (1+a/x)^x ; (1-a/x)^x |
e ; e^a ; e^-a |
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lim(x➡0) (1+x)^(1/x) ; (1+ax)^(1/x) ; (1-ax)^(1/x) |
e ; e^a ; e^-a |
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lim(x➡0) ({a^x -1}/a^x) |
= lna |
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lim(x➡0) ({e^x-1}/x) |
ln e |
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lim(x➡infinity) ({a^1/x -1}/x) |
lna |
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lim(x➡0) (ln(1+x)/x) |
1 |
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lim(x➡0) Sinx/x |
= 1 |
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lim(x➡0) tanx/x |
= 1 |
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ln base a 'b' |
ln base c 'b' / ln base c 'a' |
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Sin2x |
2tanx/(1+tan²x) |
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Cos2x |
(1-tan²x)/(1+tan²x) |
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Tan2x |
2tanx/(1-tan²x) |
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Sin3x |
3sinx - 4 sin³x |
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Cos3x |
4cos³x - 3 cosx |
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Tan3x |
= (3tanx - tan³x)/(1-3tan²x) |
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Sin A + Sin B |
2 Sin (A+B/2) Cos (A-B/2) |
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Sin A - Sin B |
2 cos( A+B/2) sin(A-B/2) |
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CosA - CosB |
-2 Sin ( A+B/2) Sin ( A-B/2) |
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CosA + CosB |
2 cos( A+B/2) cos(A-B/2) |
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Differentiation of cos ^-1 x |
-1/√1-x² |
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Differentiation of sin ^-1 x |
1/√1-x² |
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Differentiation of a^x |
a^x ln a |
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Differentiation cot^-1 |
-1/(1+x²) |
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Differentiation of sec^-1 |
1/(x×√x²-1) |
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Differentiation of cosecx inverse |
-1/(x×√x²-1) |
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Differentiation of |x| |
x/|x| or |x|/x |
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a²+x² |
Put x= a tan∅ |
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a²-x² |
Put x=asin∅ |
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x²-a² |
Put x= a sec∅ |
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Int (1/√a²-x²) dx |
Sin^-1 x/a + c |
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Int (1/√a²+x²) dx |
ln |x+√a²+x²| + c |
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Int.(1/ √x²-a² )dx |
ln |x+√x²-a²| + c |
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Int [f(x) + f'(x)] e^x dx = |
e^x × f(x) + c |
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Even function |
f(x) = f(-x) |
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Odd function |
f(x) = - f(-x) |
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Gamma function |
Gamma n = Int. (0 se infinity) e^-z z^n-1 dz |
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Int. logx |
[xlogx-x] |
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Newton raphson |
Solution of non-linear equation |
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Runga kutta |
Solution of ordinary differential equations |
R and Or |
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Simpsons rule |
Numerical integration |
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Guass elimination |
Solution of linear algebraic equations |
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