WEBVTT
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to evaluate this limit so that we can rewrite it
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into the limit. S. T. A purchase
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zero of one over T. Time squared of one
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plus t minus The square root of one plus T
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over tee times the square root of one plus T
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. Combining the two fractions. We would get limit
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. SD approaches zero of you have one minus squared
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of one plus teeth over T times the square root
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of one plus T. Now in here we would
10
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rationalize the numerator and we multiply the whole expression by
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one plus the square root of one plus T over
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one plus the square root of one busty which is
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the conjugate of the numerator. From here we would
14
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get limit esti approaches zero of You have one The
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square of the square of one plus T. Over
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. We have tee times the square root of one
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plus T times one plus the square of one plus
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T. Simplifying this, we would have limit ste
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approaches zero of one minus one plus T over Teeth
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and the squares of one plus T times one plus
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the square root of one plus T simply find further
22
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. We would get limit as T approaches zero of
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negative T over tee times square at the one plus
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T times one plus the square root of one plus
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T. And in here we can cancel out the
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tea and we would get limit S. T.
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A purchase zero of negative one over The square root
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of one plus T Times one plus the square root
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of one plastic evaluating a T. Called zero.
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We would get negative one over Squared of one plus
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0 times one plus the square root of one plus
32
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zero, which is just-1/2. And so this
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is the value of the limits.