Evaluate the Limit

Problem

(lim_t→∞)(√(,t+t2)/(3*t−t2))

Solution

1. Identify the highest power of t in the denominator to simplify the limit as t approaches infinity. The highest power is t2

2. Divide both the numerator and the denominator by t2 to normalize the expression.

3. Rewrite the numerator by bringing the t2 inside the square root as t4

(lim_t→∞)(√(,t+t2)/(t2)/(3*t−t2)/(t2))

(lim_t→∞)(√(,t/(t4)+(t2)/(t4))/((3*t)/(t2)−(t2)/(t2)))

4. Simplify the fractions inside the limit.

(lim_t→∞)(√(,1/(t3)+1/(t2))/(3/t−1))

5. Evaluate the limit by applying the property that (lim_t→∞)(1/(tn))=0 for n>0

√(,0+0)/(0−1)

0/(−1)

Final Answer

(lim_t→∞)(√(,t+t2)/(3*t−t2))=0

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