Evaluate the Limit

Problem

(lim_t→∞)(√(,t+t2)/(2*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.

√(,t+t2)/(t2)/(2*t−t2)/(t2)

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

√(,t/(t4)+(t2)/(t4))/((2*t)/(t2)−(t2)/(t2))

4. Reduce the fractions within the expression.

√(,1/(t3)+1/(t2))/(2/t−1)

5. Evaluate the limit by observing that as t→∞ terms with t in the denominator approach 0

√(,0+0)/(0−1)

6. Calculate the final numerical value.

0/(−1)=0

Final Answer

(lim_t→∞)(√(,t+t2)/(2*t−t2))=0

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