MAC $2311$

B

$(7)$

$4.$ provided.

$($a$)f(x)=sinx$ at $x=1(f(x)=(x)=(x)$

$($b$)f(x)=x^{\frac{3}{2}}$ at $x=16$ if $f(x)-\{\begin{array}{c}{x}^{\frac{1}{2}}\end{array}$

$L(x),={16}^{\frac{3}{2}}(\frac{3}{2}(16{)}^{\frac{1}{2}})(x-16),f^{\text{'}}(a)(x-a),a=16,f(16)={16}^{\frac{3}{2}}$

$,=64(\frac{3}{2}*4)(x-16),f^{\text{'}}(16)=\frac{3}{2}(16{)}^{\frac{1}{2}}$

$,=646x-96,$

$L(x),=6x-32,$

$($c$)f(x)=2^x$ at $x=0$ if $f^{\text{'}}(x)=ln(2)2^x$

$L(x)=f(a)f^{\text{'}}(a)(x-a),a=0,f(a)=2=1,f^{\text{'}}(x)=ln(2)2$

$,\{\begin{array}{c}\text{:}=ln(2)\end{array}$

$L(x)=1ln(2)(x-0)$

$L(x)=1ln(2)x$