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Tutor profile: Daniel G.

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Daniel G.
Tutor for 4 Years
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Questions

Subject: Python Programming

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Question:

Write a program to compute the sum of the elements in a list. Suppose the list is [2,8,10].

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Daniel G.
Answer:

For this problem, we need to make use of the for-loop! You can iterate over the elements of a list in Python by giving a name to the elements of the list (we are using number in the program below). The program is as follows: x = [2,8,10] sum = 0 for number in x: sum += number return sum Let's test this program out! 1. The first number is 2. Thus, sum += 2. The variable sum is 0. We add 2, thus sum = 2. 2. The second number is 8. The variable sum is 2. Thus, sum += 8 means sum = 2 + 8 = 10. 3. The last number is 10. The variable sum is 10. Thus, sum += 10 mean sum = 10 + 10 = 20.

Subject: Calculus

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Question:

What is the derivative of $$f(x) = (8x + 10)^{2}$$.

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Daniel G.
Answer:

For this problem, we must make use of the chain rule! We can view $$f(x) = (8x + 10)^{2}$$ as the following: $$f(x) = g(h(x))$$ where $$g(x) = x^2$$ and $$h(x) = (8x + 10)$$. Using the chain rule, the derivative is as follows: $$f'(x) = g'(h(x)) \times h'(x)$$. Let's break this problem into steps. 1. Compute $$g'(h(x))$$. 2. Compute $$h'(x)$$. 3. Compute $$f'(x) = g'(h(x)) \times h'(x)$$. For 1: $$g'(h(x)) = 2 \times (8x + 10).$$ For 2: $$h'(x) = 8$$. For 3: the final result is thus $$f'(x) = g'(h(x)) \times h'(x) = 2 \times (8x + 10) \times 8 = 16 \times (8x + 10) = 128x + 160.$$

Subject: Algebra

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Question:

Suppose you are given the following function: f(x) = 9x + 10. What is f(10) - f(2)?

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Daniel G.
Answer:

Let's break this problem into steps. We have been asked to evaluate f(10) - f(2). Let's thus do the following: 1. Compute f(10). 2. Compute f(2). 3. Compute f(10) - f(2). Step 1. To compute f(10), let's recall we have f(x) = 9x + 10. We substitute 10 for x and we have: f(10) = 9 * (10) + 10 = 90 + 10 = 100 = f(10). Step 2. To compute f(2), let's recall we have f(x) = 9x + 10. We substitute 2 for x and we have: f(2) = 9 * (2) + 10 = 18 + 10 = 28 = f(2). Step 3. f(10) - f(2) = 100 - 28 = 72.

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