Calculus questions, calculus homework help

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Math 161, Section 006 – Homework 11 Note: Please do these problems on your own paper so that there’s plenty of space to write legibly and show your work. This assignment is due on Thursday, May 4 at 7:00 p.m. For Problems 1-2, find the function f having the following properties, and circle your final answer. 1. f ′ (x) = 9x2 + ex , f (0) = 2 ′′ f (0) = 5, f ′ (0) = 2 2. f (x) = − cos x, 3. An arrow is shot upwards over the edge of a cliff having a height of 100 m with an initial upward velocity of 20 m/s. As it moves through the air, the arrow experiences a constant acceleration of 9.8 m/s2 toward the earth. Cliff (a) Find a formula for the height of the arrow after t seconds, and circle your final answer. (b) What is the height and velocity of the arrow at t = 3 seconds? Make it clear which answer is which, and include the proper units with your answer. (c) When is the velocity of the arrow equal to 0, and what is its height at this time? For Problems 4-7, find the exact value of the definite integral, and circle your final answer. ! 5 ! 2 1 − 2x 6. 4. (x3 + x2 + 1) dx dx x2 1 0 ! 4 ! 1 √ 3√ 5. (5ex − x) dx 7. x(x2 + x + 1) dx 2 1 0 8. Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of 8 m/s, v(t) = √ − 4 t v where t is measured in seconds. Positive values of v indicate that the particle is moving to the east, while negative values of v indicate that it is moving to the west. (a) Does the particle ever reverse its direction? If so, at what time(s)? (a) Calculate ! 1 6 6 v(t) dt, giving both an exact answer and a decimal approximation. Then, use a complete 1 sentence to explain the meaning of your answer in the context of this problem. (b) Find the total distance traveled by the particle on the time interval 1 ≤ t ≤ 6. Include units, and circle your answer. t Math 161, Section 006 – Homework 11 Note: Please do these problems on your own paper so that there’s plenty of space to write legibly and show your work. This assignment is due on Thursday, May 4 at 7:00 p.m. For Problems 1-2, find the function f having the following properties, and circle your final answer. 1. f ′ (x) = 9x2 + ex , f (0) = 2 ′′ f (0) = 5, f ′ (0) = 2 2. f (x) = − cos x, 3. An arrow is shot upwards over the edge of a cliff having a height of 100 m with an initial upward velocity of 20 m/s. As it moves through the air, the arrow experiences a constant acceleration of 9.8 m/s2 toward the earth. Cliff (a) Find a formula for the height of the arrow after t seconds, and circle your final answer. (b) What is the height and velocity of the arrow at t = 3 seconds? Make it clear which answer is which, and include the proper units with your answer. (c) When is the velocity of the arrow equal to 0, and what is its height at this time? For Problems 4-7, find the exact value of the definite integral, and circle your final answer. ! 5 ! 2 1 − 2x 6. 4. (x3 + x2 + 1) dx dx x2 1 0 ! 4 ! 1 √ 3√ 5. (5ex − x) dx 7. x(x2 + x + 1) dx 2 1 0 8. Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of 8 m/s, v(t) = √ − 4 t v where t is measured in seconds. Positive values of v indicate that the particle is moving to the east, while negative values of v indicate that it is moving to the west. (a) Does the particle ever reverse its direction? If so, at what time(s)? (a) Calculate ! 1 6 6 v(t) dt, giving both an exact answer and a decimal approximation. Then, use a complete 1 sentence to explain the meaning of your answer in the context of this problem. (b) Find the total distance traveled by the particle on the time interval 1 ≤ t ≤ 6. Include units, and circle your answer. t
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Explanation & Answer

Hey dude😊 I have the solutions ready as promisedPlease find the two attached .doc files with one containing the solutions and the other containing the concepts

1. The following kinematics formulas are useful in answering the questions
𝑖) 𝑣 = 𝑢 + 𝑎𝑡
1
𝑖𝑖) 𝑠 = 𝑢𝑡 + 𝑎𝑡 2
2
𝑖𝑖𝑖) 𝑣 2 = 𝑢2 + 2𝑎𝑠
𝑤ℎ𝑒𝑟𝑒 𝑣 = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑢 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑠 = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
2.
a) To solve this question we need to investigate if there is a direction change in the
velocity within the given time interval. This can be seen by just looking at the graph
b) To determine the time the velocity changes from positive to negative and vice versa,
we need to equate the velocity function to 0
c) Integrating over a g...


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