In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;(i) fx=1-cos 2kxx2, ifx≠0 8 , ifx=0at x = 0(ii) fx=(x-1)tanπx2, ifx≠1 k , ifx=1at x = 1(iii) fx=k(x2-2x), ifx<0 cos x, ifx≥0at x = 0(iv) fx=kx+1, ifx≤πcos x, ifx>πat x = π(v) fx=kx+1, ifx≤53x-5, ifx>5at x = 5(vi) fx=x2-25x-5,x≠5 k ,x=5at x = 5(vii) fx=kx2,x≥1 4 ,x<1at x = 1(viii) fx=k(x2+2), ifx≤03x+1 , ifx>0(ix) fx=x3+x2-16x+20x-22, x≠2k, x=2

In each of the following, find the value of the constant k so that the

1.	In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;(i) fx=1-cos 2kxx2, ifx≠0 8 , ifx=0at x = 0(ii) fx=(x-1)tanπx2, ifx≠1 k , ifx=1at x = 1(iii) fx=k(x2-2x), ifx<0 cos x, ifx≥0at x = 0(iv) fx=kx+1, ifx≤πcos x, ifx>πat x = π(v) fx=kx+1, ifx≤53x-5, ifx>5at x = 5(vi) fx=x2-25x-5,x≠5 k ,x=5at x = 5(vii) fx=kx2,x≥1 4 ,x<1at x = 1(viii) fx=k(x2+2), ifx≤03x+1 , ifx>0(ix) fx=x3+x2-16x+20x-22, x≠2k, x=2
Answer» In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; (i) $f (x) = \{\begin{cases} \frac{1 - \cos 2 k x}{x^{2}}, if & x \neq 0 \\ 8, if & x = 0 \end{cases}$ at x = 0 (ii) $f (x) = \{\begin{cases} (x - 1) \tan \frac{π x}{2}, if & x \neq 1 \\ k, if & x = 1 \end{cases}$ at x = 1 (iii) $f (x) = \{\begin{cases} k (x^{2} - 2 x), if & x < 0 \\ \cos x, if & x \geq 0 \end{cases}$ at x = 0 (iv) $f (x) = \{\begin{cases} k x + 1, if & x \leq π \\ \cos x, if & x > π \end{cases}$ at x = π (v) $f (x) = \{\begin{cases} k x + 1, if & x \leq 5 \\ 3 x - 5, if & x > 5 \end{cases}$ at x = 5 (vi) $f (x) = \{\begin{cases} \frac{x^{2} - 25}{x - 5}, & x \neq 5 \\ k, & x = 5 \end{cases}$ at x = 5 (vii) $f (x) = \{\begin{cases} k x^{2}, & x \geq 1 \\ 4, & x < 1 \end{cases}$ at x = 1 (viii) $f (x) = \{\begin{cases} k (x^{2} + 2), if & x \leq 0 \\ 3 x + 1, if & x > 0 \end{cases}$ (ix) $f (x) = \{\begin{cases} \frac{x^{3} + x^{2} - 16 x + 20}{{(x - 2)}^{2}}, x \neq 2 \\ k, x = 2 \end{cases}$

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