How do you prove that #g(x) = 1/2x# is continuous at #x=1/4#?

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Answer 1 · 2017-11-25T17:45:47

Please refer to the Explanation.

To prove that the function #g(x)=1/2x# is continuous at #x=1/4,# we

have to show that, #lim_(x to 1/4) g(x)=g(1/4).#

Now, #lim_(x to 1/x) g(x),#

#=lim_(x to 1/4) 1/2x,#

#=1/2*1/4,#

#=1/8,#

#=g(1/4).#

Hence, #g# is continuous at #x=1/4.#