Question

Evaluate: lim x tends to 4 x⁴ - 64x ÷ √x²+9 - 5​

Answer 1

Given :  Lim x→4  (x⁴  - 64x )/(√(x²+9)  - 5​ )

To Find : Evaluate

Solution:

Lim x→4  (x⁴  - 64x )/(√(x²+9)  - 5​ )

Put x = 4

=   (4⁴  - 64*4 )/(√(4²+9)  - 5​ )

= (256 -  256)/ (√25 - 5)

= 0/(5 - 5)

= 0/0

as its 0/0 form

we can apply L'hospital Rule

(x⁴  - 64x )/(√(x²+9)  - 5​ )

= (4x³ - 64) /(2x/2√(x²+9) )

= 4(x³ - 16)√(x²+9)/x

x = 4

= 4(4³  - 16) √(4²+9)/4

= (64 - 16)√25

= 48(5)

= 240

Lim x→4  (x⁴  - 64x )/(√(x²+9)  - 5​ ) = 240

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