Exam (elaborations)
MCV4U Unit # 4 – Extensions Assessment of Learning 2021/2022
- Course
- Institution
MCV4U Unit # 4 – Extensions Assessment of Learning Assessment of Learning Unit # 4 – Extensions 1 a. Find lim
[Show more]
Content preview
Unit # 4 – Extensions MCV4U Unit # 4 – Extensions Assessment of Learning Assessment of Learning Unit # 4 – Extensions 1 a. Find lim𝑥→0−2 sin 3𝑥 . Defend your answer. (2 marks) Consider this graph. From the graph we see the y value approaches 0, the x value approaches 0 from both left and right side. Therefore we know lim
𝑥→0−2sin3𝑥 = (−2)(0)= 0 1.b Find lim
𝑥→0−𝑐𝑜𝑠5𝑥 . Defend your answer. (2 marks) Consider this graph. From the graph we see the Y value approach 1, the x value approaches o from both the right and left side. Therefore, lim
𝑥→0−𝑐𝑜𝑠5𝑥 = (−1)(1)= 1 . Unit # 4 – Extensions 2. Find the derivative
a.𝑦 = 𝑠𝑖𝑛𝑥5 (1 mark)
𝑦′=(𝑠𝑖𝑛𝑥5)′ 𝑦′= cos 𝑥5(𝑥5)′ 𝑦′= cos 𝑥5(5𝑥5−1) 𝑦′= 5𝑥4cos 𝑥5 b.𝑦 = sin5𝑥 (1 mark)
𝑦′= (sin5𝑥)′ 𝑦′= 5 sin5−1𝑥(𝑠𝑖𝑛𝑥)′ 𝑦′= 5 sin4𝑐𝑜𝑠𝑥 c.𝑦 = cos(4𝑥 + 9 ) (1 mark)
𝑦′= (cos (4𝑥 + 9)′ 𝑦′= − sin (4𝑥 + 9)(4𝑥 + 9) 𝑦′= − 𝑠𝑛(4𝑥 + 9 )(4) 𝑦′= −4 sin(4𝑥 + 9) ∴ The derivative of 𝑦=𝑠𝑖𝑛𝑥5 is 𝑦′=5𝑥4cos𝑥5 ∴ The derivative of 𝑦=sin5𝑥 is 𝑦′=5sin4𝑐𝑜𝑠𝑥 ∴ The derivative of 𝑦=cos(4𝑥+9) is 𝑦′=−4sin(4𝑥+9) Unit # 4 – Extensions d.𝑦 = cos2(𝑥2+ 3) (2 marks)
𝑦′= (cos2(𝑥2+ 3))′ 𝑦′= 2 cos(𝑥2+ 3)(cos(𝑥2+ 3) 𝑦′= 2cos (𝑥2+ 3)(−sin (𝑥2+ 3)(𝑥2+ 3) 𝑦′= 2co s (𝑥2+ 3)(−sin (𝑥2+ 3)(𝑥2+ 3)′ 𝑦′= −2cos (𝑥2+ 3)𝑠 in (𝑥2+ 3)(2𝑥) 𝑦′= −4𝑥 cos (𝑥2+ 3)𝑠 in (𝑥2+ 3) e.𝑦 = 𝑥2sin(𝑥2+ 5) (3 marks)
𝑦′ = 𝑥2sin(𝑥2+ 5) ′ 𝑦′= 𝑥2(sin(𝑥2+ 5)′+ sin(𝑥2+ 5)(𝑥2)′ 𝑦′= 𝑥2cos (𝑥2+ 5)(𝑥 62+ 5)′ + sin(𝑥2+ 5)(2𝑥2−1) 𝑦′= 𝑥2cos(𝑥2+ 5) (2𝑥)+ sin (𝑥2+ 5)(2𝑥) 𝑦′= 2𝑥3cos(𝑥2+ 5)+ 2𝑥 sin(𝑥2+ 5) ∴ The derivative of 𝑦=cos2(𝑥2+3) is 𝑦′=−4𝑥 cos(𝑥2+3)𝑠in(𝑥2+3) ∴ The derivative of 𝑦=𝑥2sin(𝑥2+5) is 𝑦′=2𝑥3cos(𝑥2+5)+2𝑥sin(𝑥2+5)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller GEEKA. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81531 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now