Using limits can you please help me with this?

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(a){:[y=f(x)=3x^(2)-2x+5],[((dy)/(dx))_(x=1)=lim_(x rarr1)(f(x)-f(1))/(x-1)],[=lim_(x rarr1)(3x^(2)-2x+5-(3*1^(2)-2*1+5))/(x-1)],[=lim_(x rarr1)(3x^(2)-2x+5-(3-2+5))/(x-1)],[=lim_(x rarr1)(3x^(2)-2x-1)/(x-1)],[=lim_(x rarr1)(3x^(2)-3x+x-1)/(x-1)]:}{:[=lim_(x rarr1)(3x(x-1)+1(x-1))/(x-1)],[=lim_(x rarr1)((3x+1)(x-1))/((x-1))],[=lim_(x rarr1)quad3x+1],[((dy)/(dx))=1],[=4=4(1)=3-2+5=6]:}Conation of tangent like at (x,y,(y-y_(0))=((dy)/(dx))_(u=x_(0))(x-x_(0))at (1,6){:[y-6=4(x-1)],[y-4x=2]:}(6) g(x)=(1)/(2x+3){:[((dy)/(dx))_(x=0)=lim_(x rarr0)(g(x)-g(0))/(x-20)],[=lim_(x rarr0)((1)/(2x+3)-(1)/(3))/(x)],[=lim_(x ra ... See the full answer