Question

find the value if limit x tends to 3 what is the answer to the attached question




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Answer 1

Step-by-step explanation:

=> (x√x - 3√3)/sin(x - 3)

Rationalize the numerator,

=> (x√x - 3√3)(x√x + 3√3)/(x√x + 3√3)sin(x - 3)

=> (x³ - 3³)/(x√x + 3√3)sin(x - 3)

=> (x - 3)(x² + 3x + y²)/(x√x + 3√3)sin(x - 3)

=> [(x² + 3x + y²)/(x√x + 3√3)] * [(x - 3)/sin(x - 3)]

Hence, limit(x→3) = limit(x - 3 → 0) of (x - 3)/sin(x - 3) comes out to be 1.

=> lim(x→3) (x² + 3x + y²)/(x√x + 3√3) * 1

=> (3² + 3(3) + 3²)/(3√3 + 3√3)

=> 27/6√3

=> 3√3/2 or 1.5√3