Question

How how to find the limit of (x)={2x+1,for x<2,{x²+1,for x>2

Answer 1

Answer:

f(x) { 2x + 1 for x< 2 }

{ x^2 + 1 for x > 2 }

let us find the limiting value of x as it approaches 2 from left hand side

lim ₓ→₂ ᶠʳᵒᵐ ˡᵉᶠᵗ = 2(2) + 1 = 5

now let us find the limiting value from the right hand side

lim ₓ→₂ ᶠʳᵒᵐ ʳⁱᵍʰᵗ = 2² + 1 = 5

As the limiting value is same from left and from right, the limit exists which is 5