Question

Q1) Find the limit of the function by using direct substitution.:

Answer 1

Q1)
For the first question, the function is 
                                  f(x)=3eˣ * cos(x)
Now, 
         $\lim_{x \to \\\frac{ \pi }{2} } 3e^x cos(x)$
By direct substitution of π/2,
we get,
         = $3e^ \frac{ \pi }{2} cos( \frac{ \pi }{2} )$   , as cos(π/2)=0
         = 0 

Q2)
For the second question, the function is 
                         f(x)= x²-1
Now,
            $\lim_{x\to \ 0} x^{2} -1$
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,
                       
                = $\lim_{x\to \ 0} x^{2} +\frac{3}{ x^4 }$  
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.
                = $\lim_{x\to \ 0} x^{2} +\lim_{x\to \ 0} \frac{3}{ x^4 }$
                = infinity   is the correct answer.