limits and continuity

lim x→0 (sinx)/x

1

lim x→0 (1-cosx)/x

0

lim x→0 sin(ax)/ax

1

lim x→0 ax/sin(ax)

1

lim x→0 sin(ax)/bx

a/b

lim x→0 ax/sin(bx)

a/b

lim x→0 x/sinx

1

lim x→0 sin(ax)/sin(bx)

a/b

lim x→0 tan(ax)/ax

1

lim x→0 ax/tan(bx)

a/b

lim x→0 ax/tan(ax)

1

lim x→0 tan(ax)/tan(bx)

a/b

lim x→0 tan(ax)/bx

a/b

lim x→0 sin(ax)/tan(bx)

a/b

lim x→∞ [1+1/x]^x

e

lim x→0 (1+x)^(1/x)

e

lim x→∞ [1+1/f(x)]^f(x)

e

lim x→0 (1+f(x))^(1/f(x))

e