Discuss the continuity of the following functions at the indicated point(s):(i) fx=x cos1x,x≠0 0 ,x=0at x=0(ii) fx=x2sin1x,x≠0 0 ,x=0at x=0(iii) fx=(x-a)sin1x-a,x≠a 0 ,x=aat x=a(iv) fx=ex-1log(1+2x), ifx≠a 7 , ifx=0at x=0(v) fx=1-xn1-x,x≠1n-1 ,x=1n∈Nat x=1(vi) fx=x2-1x-1, forx≠1 2 , forx=1at x=1(vii) fx=2x+x2x,x≠0 0 , x=0at x=0(viii) fx=x-asin1x-a, for x≠a0, for x=aat x=a

Discuss the continuity of the following functions at the indicated poi

1.	Discuss the continuity of the following functions at the indicated point(s):(i) fx=x cos1x,x≠0 0 ,x=0at x=0(ii) fx=x2sin1x,x≠0 0 ,x=0at x=0(iii) fx=(x-a)sin1x-a,x≠a 0 ,x=aat x=a(iv) fx=ex-1log(1+2x), ifx≠a 7 , ifx=0at x=0(v) fx=1-xn1-x,x≠1n-1 ,x=1n∈Nat x=1(vi) fx=x2-1x-1, forx≠1 2 , forx=1at x=1(vii) fx=2x+x2x,x≠0 0 , x=0at x=0(viii) fx=x-asin1x-a, for x≠a0, for x=aat x=a
Answer» Discuss the continuity of the following functions at the indicated point(s): (i) $f (x) = \{\begin{cases} \|x\| \cos (\frac{1}{x}), & x \neq 0 \\ 0, & x = 0 \end{cases} at x = 0$ (ii) $f (x) = \{\begin{array}{l} x^{2} \sin (\frac{1}{x}), & x \neq 0 \\ 0, & x = 0 \end{array} at x = 0$ (iii) $f (x) = \{\begin{array}{l} (x - a) \sin (\frac{1}{x - a}), & x \neq a \\ 0, & x = a \end{array} at x = a$ (iv) $f (x) = \{\begin{array}{l} \frac{e^{x} - 1}{\log (1 + 2 x)}, if & x \neq a \\ 7, if & x = 0 \end{array} at x = 0$ (v) $f (x) = \{\begin{array}{l} \frac{1 - x^{n}}{1 - x}, & x \neq 1 \\ n - 1, & x = 1 \end{array} n \in N at x = 1$ (vi) $f (x) = \{\begin{cases} \frac{\|x^{2} - 1\|}{x - 1}, for & x \neq 1 \\ 2, for & x = 1 \end{cases} at x = 1$ (vii) $f (x) = \{\begin{array}{l} \frac{2 \|x\| + x^{2}}{x}, & x \neq 0 \\ 0, & x = 0 \end{array} at x = 0$ (viii) $f (x) = \{\begin{cases} \|x - a\| \sin (\frac{1}{x - a}), for x \neq a \\ 0, f o r x = a \end{cases} at x = a$