sendetimejhn
Answered question
2022-03-25
Given that lim_(x->2)f(x)=7,g is continuous at 3, and lim_(x->3)g(x)=3, find the limit lim_(x->2)(xf(x)-x^3)/(g(x+1))
Answer & Explanation
RizerMix
Expert2022-05-03Added 656 answers
Split the limit using the Limits Quotient Rule on the limit as approaches .
Split the limit using the Sum of Limits Rule on the limit as x approaches .
Split the limit using the Product of Limits Rule on the limit as approaches .
Move the exponent from outside the limit using the Limits Power Rule.
Evaluate the limits by plugging in for all occurrences of .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Add and .
Simplify the numerator.
Raise to the power of .
Multiply by .
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