Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers. limx→31x2+2x−115x−3

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Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.  limx→31x2+2x−115x−3

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Concept:  The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.  Given:  limx→31x2+2x−115x−3  Solution:  Thus the given function is as follows,  limx→31x2+2x−115x−3  Computing the limit by simplifying the function as follows, limx→ax2−a2x−a=limx→a((x+a)(x+a))  limx→ax2−a2x−a=limx→a(x−a)(x+a)x−a  =limx→a((x)2−(a)2)(x+a)x−a  limx→a((x+x)(x+a))  limx→ax2−a2x−a=limx→a((x+a)(x+a))  =(a+a)(a+a)=2a(2a)  =2aa

Find the following limits or state that they do not exist. Assume a, b, c, and k

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