Calculus Answers

f³f¹(x) = √secx.x³

f(x) = √(cosx) + √(sinx) dx

f(x) = √(tanx) + √(sinx) dx

f(x) = √(cotx.x³) dx

Find the area of the region inside the circle r=2sinθ and outside the circle r=1.

Find the area enclosed by the curve r(θ)=1+2sinθ and the rays θ=0 and θ=π3

Given that M =

2 −1
−3 4 !
and that M^2 − 6M + kI = 0, find k.

2.Your favourite musician is on the cover of a current magazine. To preserve this photo, you decide to carefully cut it out and frame it. The frame is going to go on the outer edge and you want to make it out of a special strip of wood. Before you go to purchase this wood, you need to know how much you will need. The dimensions of the photo are 36 cm in length and 24 cm in width. Determine how much of the stip of wood you will need. (2 marks)



3. Jack wants to fence his rectangular backyard. The backyard is 20 metres long and 40 metres wide. The cost of materials for the fence is $10 per metre.
a) How much is the total cost of putting the fence around the backyard. (2 marks)

Your favourite musician is on the cover of a current magazine. To preserve this photo, you decide to carefully cut it out and frame it. The frame is going to go on the outer edge of the photo and you want to make it out of a special strip of wood. Before you go to purchase this wood, you need to know how much you will need. The dimensions of the photo are 36 cm in length and 24 cm in width. Draw a diagram below of the photo and determine how much of the strip of wood you will need.


Jack wants to fence his rectangular backyard. The backyard is 20 metres long and 40 metres wide. The cost of materials for the fence is $10 per metre.

How much is the total cost of putting the fence around the backyard. (2 marks)










Jack also wants to cover his backyard with grass. Grass costs $2 per square metre, how much will it cost to fill the backyard. (2 marks)

Given: y=2x^2/x^2-1
Find:
1. the X and y intercepts
2. the vertical, horizontal and oblique asymptotes
3. local maximum and the local minimum.
4. limit as x goes to positive infinity.