Exercises for Question Type 3: Finding the tangent and normal to more complex functions using the GDC at different points - IB | RevisionDojo

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

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

Question 1

(No specification provided)

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

[6]

Question 2

Find the equations of the tangent and normal to the curve $y = e^x \ln(x^2+1)$ at $x = 0$ .

[5]

Question 3

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

[8]

Question 4

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

[6]

Question 5

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

[8]

Question 6

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

[7]

Question 7

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

[7 marks]

[7]

Question 8

Find the equations of the tangent and normal to the curve $y = (2x+1)e^{x^2}$ at $x = 0$ .

[6]

Question 9

Find the equations of the tangent and normal to the curve $y = x^2e^{3x}$ at $x = 0$ .

Find the equations of the tangent and normal to the curve $y = x^2e^{3x}$ at $x = 0$ . [5 marks]

[5]

Question 10

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

[7]

Question 11

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

[7]