Question Type 3: Finding the tangent and normal to more complex functions using the GDC at different points Exercises

Find the equations of the tangent and normal lines to the curve $y=\ln(x^2+1)$ at $x=1$.

Find the equations of the tangent and normal lines to the curve $y = e^{x^2}$ at $x = 1$.

Find the equations of the tangent and normal lines to the curve $y = x^2e^{-x}$ at $x = 0.5$.

Find the equations of the tangent and normal lines to the curve $y = x^3\ln x$ at $x = 2$.

Find the equations of the tangent and normal lines to the curve $y = \ln(\sin x) + x^2$ at $x = \pi/4$.

Find the equations of the tangent and normal lines to the curve $y = e^{2x}\\ln x + 5x^3$ at $x = 1$.

Find the equations of the tangent and normal lines to the curve $y=\frac{x+1}{x-1}+e^x$ at $x=2$.

Find the equations of the tangent and normal lines to the curve $y=\sqrt{x}\,e^{3x}$ at $x=4$.

Find the equations of the tangent and normal lines to the curve $y = x^x$ at $x = 2$.

Find the equations of the tangent and normal lines to the implicitly defined curve $x^2+xy+y^2=7$ at the point $(1,2)$.

Find the equations of the tangent and normal lines to the curve $y=x^x+e^x$ at $x=1$.

Find the equations of the tangent and normal lines to the parametric curve $x=t^2-1,\;y=\ln t$ at $t=1$.