Find the following limits or state that they do not exist. limw→1a⋅1(w2−2)−1(w−1)b

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Neelam Wainwright · Accepted Answer

Given,  limw→1a⋅1w2−2−1(w−1)b  Rewrite the function:  lims→1−1(as2−s−bs−1)=lims→1−1a−bss(s−1)  The limit of product/quotient is the product/quotient of limits:  lims→1−1a−bss(s−1)=lims−&amp;gt;1−1a−bss⋅lims−&amp;gt;1−11s−1  The limit of a quotient is the quotient of limits:  lims→1−1(a−bs)s⋅lims→1−11s−1=lims→1−11s−1⋅lims→1−1a−bslims→1−1s  Substitete the variable with the value:  lims→1−11s−1⋅lims→1−1(a−bs)lims−&amp;gt;1−1s=lims→1−11(s−1)⋅(a−b)lims→1−1s  Substitete the variable with the value:  (a−b)lims→1−11s−1⋅lims→1−1s−1=(a−b)lims→1−11s−1⋅1−1  The function decreases without a bound:  lims→1−11s−1=−∞  Therefore,  lims→1−1as2−s−bs−1=−∞(a−b)  Rewrite the function:  lims→11as2−s−bs−1=lims→11a−bss(s−1)  The limit of a product/quotient is the product/quotient of limits:  lims→11a−bss(s−1)=lims→11a−bss⋅lims→11(1s−1)  The limit of quotient is the quotient of limits:  lims−&amp;gt;111s−1⋅lims→11a−bss=lims→111s−1lims→11a−bslims→11s  Substitute variable with the value:

Find the following limits or state that they do not exist. lim_{wrightarrow1}frac{acdot1}{(w^2-2)}-frac{1}{(w-1)b}

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New Questions in Calculus 1