Q1)
For the first question, the function is
f(x)=3eˣ * cos(x)
Now,
[tex] \lim_{x \to \\\frac{ \pi }{2} } 3e^x cos(x)[/tex]
By direct substitution of π/2,
we get,
= [tex] 3e^ \frac{ \pi }{2} cos( \frac{ \pi }{2} )[/tex] , as cos(π/2)=0
= 0
Q2)
For the second question, the function is
f(x)= x²-1
Now,
[tex] \lim_{x\to \ 0} x^{2} -1 [/tex]
By direct substitution,
the square term will be zero and the answer is -1
= 0 -1
=-1
Q3)
For the third question, the function is
f(x)=x²+3/x⁴
Now,
= [tex] \lim_{x\to \ 0} x^{2} +\frac{3}{ x^4 } [/tex]
Now, by using the property of limit separate the limit with both x² and 3/x⁴
the x² term will be zero and the second term will approach infinity.
= [tex]\lim_{x\to \ 0} x^{2} +\lim_{x\to \ 0} \frac{3}{ x^4 }[/tex]
= infinity is the correct answer.
