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Gala2k [10]
4 years ago
14

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

Mathematics
1 answer:
Nonamiya [84]4 years ago
6 0
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.

         
                        
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