University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

59

Pages:

5
Author:

Bailey Ayala

Question 1 Limits and Asymptotes of the Given Graph: (a) lim ⁡ 𝑥 → ∞ 𝑓 ( 𝑥 ) = 2 lim x→∞ f(x)=2 (b) lim ⁡ 𝑥 → − ∞ 𝑓 ( 𝑥 ) = − 2 lim x→−∞ f(x)=−2 (c) lim ⁡ 𝑥 → 1 + 𝑓 ( 𝑥 ) = ∞ lim x→1 + f(x)=∞ (d) lim ⁡ 𝑥 → 1 − 𝑓 ( 𝑥 ) = − ∞ lim x→1 − f(x)=−∞ (e) Vertical asymptote: 𝑥 = 1 x=1 Horizontal asymptote: 𝑦 = 2 , 𝑦 = − 2 y=2,y=−2 Question 2 Volume of Solid by Revolution: The given curve is 𝑦 = 1 , 𝑥 = 0 , 𝑥 = 4 tan ⁡ ( 𝜋 3 𝑦 ) y=1,x=0,x=4tan( 3 π y). The volume of the solid generated by revolving the shaded region about the 𝑦 y-axis is: 𝑉 = 48 ( 3 − 𝜋 3 ) V=48( 3 − 3 π ) Question 3 Rectangular to Polar Equation: Given 𝑥 𝑦 = 5 xy=5, convert to polar form: 𝑟 2 = 10 sin ⁡ ( 2 𝜃 ) r 2 = sin(2θ) 10 Question 4 Finding 𝛿 δ: For ∣ 𝑥 − 1 ∣ < 𝛿 ∣x−1∣<δ, ∣ 𝑓 ( 𝑥 ) − 1 ∣ < 0.2 ∣f(x)−1∣<0.2, we find 𝛿 = 0.1 δ=0.1. Question 5 Function 𝑓 ( 𝑥 ) f(x) and Tangent Line: The function 𝑓 ( 𝑥 ) f(x) such that 𝑓 ′ ( 𝑥 ) = 3 𝑥 2 f ′ (x)=3x 2 and the line 8 𝑥 + 𝑦 = 0 8x+y=0 is tangent to 𝑓 ( 𝑥 ) f(x): 𝑓 ( 𝑥 ) = 3 4 𝑥 4 + 729 4 f(x)= 4 3 x 4 + 4 729