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MATH 1300 Lecture Notes - Lecture 2: Power Rule, Differentiable Function

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11 Sep 2018

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York University

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Mathematics and Statistics

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MATH 1300 verified notes

MATH 1300 Lecture Notes - Lecture 1: Constant Function, Power Rule

MATH 1300 Lecture Notes - Lecture 2: Power Rule, Differentiable Function

MATH 1300 Lecture 3: MATH 1300 Lecture 3 Notes – Exponential Function and Derivative of the Natural Exponential Function

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Math 1300 lecture 2 notes power rule and new derivatives from old. In example we found that: which can be written as, this sho(cid:449)s that the po(cid:449)e(cid:396) rule is t(cid:396)ue e(cid:448)e(cid:374) (cid:449)he(cid:374) (cid:374) (cid:1005)(cid:1006). In fact, we will show that it is true for all real numbers n: the power rule (general version), if n is any real number, then, example, differentiate, solution: It also enables us to find normal lines: the normal line to a curve c at a point p is the line through p that is perpendicular to the tangent line at p. New derivatives from old: when new functions are formed from old functions by addition, subtraction, or multiplication by a constant, their derivatives can be calculated in terms of derivatives of the old functions. In particular, the following formula says that the derivative of constant times a function is the constant times the derivative of the function.

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Related Questions

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1.Create a list that contains 10 successive integers starting with the value in the variable start. For example, if start is 7, the resulting list should be [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. Store the list in a variable named my_list. Assume that the value of start has already been set.

2.Create a list that is made up of the first half of the elements of a list called original_list. Store the new list in a variable called half_list. Assume that the original list has already been initialized and contains an even number of elements.

3. Write a predicate function called same_ends that accepts a list of integers and an integer (n) as arguments. Return True if the first n numbers in the list are the same as the last n numbers in the list, and False otherwise. For example, if the list was [1, 2, 3, 4, 99, 1, 2, 3, 4], the function would return True if n is 4 and False if n is 3. Assume that n is between 1 and the length of the list, inclusive.

4.Write a function called highest_values that accepts as arguments a list of numeric values and a single integer (n). The function should return a list made up of the largest n values from the argument list in order from lowest to highest. For example, if the argument list is [46, 82, 25, 61, 70, 33, 54] and n is 3, the return value should be [61, 70, 82]. Assume that the argument list contains at least n elements.

5.Assume that a list of integers stored in a variable named original contains exactly two elements that are zero. Write code that creates a separate list that contains the elements from original that are between the two zeros. Do not include the zeros in the new list. Store the list in a variable named between_zeros.

6. Write a function called price_range that accepts a list of floating-point numbers representing prices as an argument and returns the the difference between the highest price and the lowest price. Do NOT use the built-in functions max or min in your solution. Assume that all prices are positive values and that none of them exceed 10,000.00.

7. Write a function called count_vowels that accepts a string argument that represents a word and returns the number of vowels that are in the word. The vowels are A, E, I, O, and U (ignore the 'sometimes Y' rule). Count both uppercase and lowercase vowels.

Assume that the variable table holds a two-dimensional list of integers. Write code that computes the sum of all elements in the table, assigning the result to the variable table_sum.

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