" 9."Lt_(x=0)(x cos x-log_(e)(1+x))/(x^(2))

Let f(x)=(e^(x)x cos x-x log_(e)(1+x)-x)/(x^(2)),x!=0 If f(x) is continuous at x=0, then f(0) is equal to

underset(x to 0)"Lt" (x cos -log(1+x))/(x^(2))=

Lt_(xto0)(xcosx-ln(1+x))/x^(2)

Show that Lt_(x to 0)(log(1+x))/(x^(2))=1

Lt_(x to 0)(1-cos(x^(0)))/(x^(2))=

Lt_(x to 0)log_(2x)x=

Evaluate the following limits : Lt_(xto0)(log_(e)(1+5x))/x

Evaluate Lt_(x to 0)(log(1 + 5x))/(x)