## Limits and derivatives – Exercise 13.1 – Class XI

Evaluate the given lim┬(x→3)⁡〖x+3〗

Evaluate the given limit: 〖lim┬(x→π) (〗⁡〖x-22/7)〗

Evaluate the given limit: lim┬(x→1)⁡〖〖πr〗^2 〗

Evaluate the given limit: lim┬(x→4) (4x+3)/(x-2)

Evaluate the given limit: 〖lim┬(x→-1) (〗⁡〖(x^10+x^5+1)/(x-1))〗

Evaluate the given limit: lim┬(x→0) (〖(x+1)〗^5-1)/x

Evaluate the given limit: lim┬(x→2) (〖3x〗^2-x-10)/(x^2-4)

Evaluate the given limit: lim┬(x→2) (x^4-81)/(〖2x〗^2-5x-3)

9. Evaluate the given limit: lim┬(x→0) (ax+b)/(cx+1)

Evaluate the given limit: lim┬(z→1) z^(1/3)/z^(1/6)

11. Evaluate the given limit: lim┬(x→1) (ax^2+bx+c)/(cx^2+bx+a),a+b+c ≠0

Evaluate the given limit lim┬(x→-2) (1/x+1/2)/(x+2)

Evaluate the given limit lim┬(x→0) sinax/bx

Evaluate thegivven limit lim┬(x→0) sinax/sinbx,a,b≠0

Evaluate the given limit lim┬(x→π) sin⁡(π-x)/π(π-x)

Evaluate the given limit lim┬(x→0) cosx/(π-x)

Evaluate the given limit lim┬(x→0) (cos2x-1)/(cosx-1)

Evaluate the given limit lim┬(x→0) (ax+xcosx)/bsinx

Evaluate the given limit lim┬(x→0) xsecx

Evaluate the given limit 〖lim〗┬(x→0) (sinax+bx)/(ax+sinbx),a,b,a+b≠0

Evaluate the given limit lim┬(x→0) (cosecx-cotx)

lim┬(x→π/2) tan2x/(x-π/2)

Find lim┬(x→0) f(x) lim┬(x→1) f(x),where f(x)={█(2x+3, x≤0@3(x+1), x>0)┤

Find lim┬(x→1) f(x),where f(x)={█(x^2-1, x≤0@〖-x〗^2-1, x>1)┤

Evaluate lim┬(x→0) f(x) , where f(x) = {█((|x|)/x, x≠0@0, x=0)┤

Find lim┬(x→0) f(x),where f(x)= {█(x/|x| , x≠0@0, x=0)┤

Find lim┬(x→5) f(x),where f(x)=|x|-5

Suppose f(X) = {█(a+bx, x1)┤ and lim┬(x→1) f(x)=f(1)what are possible values of a and b?

If f(x)= {█(|x|+1, x<0@0, x=0@|x|-1, x>0)┤ For what value of a does lim┬(x→a) f(x) exists?