76 Higher Engineering Mathematics
Hence lim
x→ 0{
x−sinx
x−tanx}
=−1
2Now try the following exerciseExercise 34 Further problems on limiting
valuesDetermine the following limiting values- lim
x→ 1
{
x^3 − 2 x+ 1
2 x^3 + 3 x− 5}[
1
9]- lim
x→ 0
{
sinx
x}
[1]- lim
x→ 0
{
ln( 1 +x)
x}
[1]- lim
x→ 0
{
x^2 −sin3x
3 x+x^2}
[−1]- lim
θ→ 0
{
sinθ−θcosθ
θ^3}[
1
3]- lim
t→ 1
{
lnt
t^2 − 1}[
1
2]- lim
x→ 0
{
sinhx−sinx
x^3}[
1
3]- lim
θ→π 2
{
sinθ− 1
lnsinθ}
[1]- lim
t→ 0
{
sect− 1
tsint}[
1
2]