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 $y = \ln(\sin x) + x^2$ at $x = \frac{\pi}{4}$.

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 curve $y = x^2e^{-x}$ at $x = 0.5$.

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 $y = e^{2x}\ln x + 5x^3$ 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 $y = x^3 \ln x$ at $x = 2$.

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

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 $y = \ln(x^2 + 1)$ at $x = 1$.

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

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