{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

calculus-exam-solutions

calculus-exam-solutions - MATH1020 Past Exam Questions...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH1020 Past Exam Questions Calculus For the last three lectures, Oreste went through some solutions to past exams. I actually wasn't at UNI for the last week (except on Monday), so I have had to borrow notes from Gareth, I'm fairly confident that Gareth's note taking ability is above average, so it should be OK. Also thanks to Gareth for lending them to me. I'm going to put all the questions in this one document because Gareth doesn't have dates in his notes and they all sort of merge together. Yeah. From Gareth's notes it seems that Oreste just outlined the way to solve some of the questions without going into detail, I'll try stay as true to Gareth's notes as I can. All these questions can be found on the MATH1020 page under “Exercises & Solutions”, it's titled “Past Exam Questions”. Also there will be no sketching in the exam! Hooray! I hate sketching... Semester 1 2008 1. a) By the extreme value theorem. b) f ' x = 1 2cos x f ' x = 0 cos x = 1 2 x = ± 3 Now test − , 3 , 3 , to find the global and local max/min (first part solved). Now test the intervals: x [ − , 3 3 ] , f ' x  0 x [ − 3 3 , 3 3 ] , f ' x  0 x [ 3 3 , ] , f ' x  0 From which we can tell where f is increasing and decreasing (second part solved). We can use the intermediate value theorem to show that there is only one point between each local max and min (and hence there are only 3 points in total) (last part solved). c) f ' ' x = 2sin x Concave up between [ 0, ] concave down between [− , 0 ] Point of inflection at 0.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
d) x n 1 = x n f x n f ' x n x 1 = 3 4 3 4 2sin 3
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}