2.3 Differentiabilityap Calculus
2021年3月5日Download here: http://gg.gg/ojk8z
CHAPTER 2 Differentiation Section 2.1 The Derivative and the Tangent Line Problem 95 1. (a) At slope At slope (b) At slope At slope x2, y 2, 2. By Rolle’s Theorem, there must be at least one c in (-2, 3) such that g’(c) = 0. Practice Problems Determine the interval(s) on which the following functions are continuous and the interval(s) on which they are differentiable. The notion of continuity and differentiability is a pivotal concept in calculus because it directly links and connects limits and derivatives. We have already learned how to prove that a function is continuous, but now we are going to expand upon our knowledge to include the idea of differentiability. In other words, we’re going to. Live: Biden on the verge of reaching 270 electoral votes. Anne Hathaway apologizes to disability community. Did the 49ers swing a local California election? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
(1) Find the derivatives of the following functions using first principle.
(i) f(x) = 6Solution
(ii) f(x) = -4x + 7Solution
(iii) f(x) = -x2 + 2 Solution
(2) Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?
(i) f(x) = |x - 1|Solution
(ii) f(x) = √(1 - x2) Solution
(3) Determine whether the following function is differentiable at the indicated values.
(i) f(x) = x | x | at x = 0 Solution
(ii) f(x) = |x2 - 1| at x = 1 Solution
(iii) f(x) = |x| + |x - 1| at x = 0, 1 Solution
(iv) f(x) = sin |x| at x = 0 Solution
(4) Show that the following functions are not differentiable at the indicated value of x.
(i)
Solution
(5) The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.
Solution
(6) If f(x) = |x + 100| + x2, test whether f’(-100) exists.
(7) Examine the differentiability of functions in R by drawing the diagrams.
(i) | sin x | Solution
(ii) |cos x| Solution
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ALGEBRA
Negative exponents rules
COMPETITIVE EXAMS
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
WORKSHEETS
TRIGONOMETRY
Trigonometric identities
MENSURATION
GEOMETRY
COORDINATE GEOMETRY
CALCULATORS
MATH FOR KIDS
LIFE MATHEMATICS
SYMMETRY
CONVERSIONS
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
OTHER TOPICS 2.3 Differentiabilityap Calculus Definition
Ratio and proportion shortcuts
Converting repeating decimals in to fractions2.3 Differentiabilityap Calculus Notes
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CHAPTER 2 Differentiation Section 2.1 The Derivative and the Tangent Line Problem 95 1. (a) At slope At slope (b) At slope At slope x2, y 2, 2. By Rolle’s Theorem, there must be at least one c in (-2, 3) such that g’(c) = 0. Practice Problems Determine the interval(s) on which the following functions are continuous and the interval(s) on which they are differentiable. The notion of continuity and differentiability is a pivotal concept in calculus because it directly links and connects limits and derivatives. We have already learned how to prove that a function is continuous, but now we are going to expand upon our knowledge to include the idea of differentiability. In other words, we’re going to. Live: Biden on the verge of reaching 270 electoral votes. Anne Hathaway apologizes to disability community. Did the 49ers swing a local California election? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
(1) Find the derivatives of the following functions using first principle.
(i) f(x) = 6Solution
(ii) f(x) = -4x + 7Solution
(iii) f(x) = -x2 + 2 Solution
(2) Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?
(i) f(x) = |x - 1|Solution
(ii) f(x) = √(1 - x2) Solution
(3) Determine whether the following function is differentiable at the indicated values.
(i) f(x) = x | x | at x = 0 Solution
(ii) f(x) = |x2 - 1| at x = 1 Solution
(iii) f(x) = |x| + |x - 1| at x = 0, 1 Solution
(iv) f(x) = sin |x| at x = 0 Solution
(4) Show that the following functions are not differentiable at the indicated value of x.
(i)
Solution
(5) The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.
Solution
(6) If f(x) = |x + 100| + x2, test whether f’(-100) exists.
(7) Examine the differentiability of functions in R by drawing the diagrams.
(i) | sin x | Solution
(ii) |cos x| Solution
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
ALGEBRA
Negative exponents rules
COMPETITIVE EXAMS
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
WORKSHEETS
TRIGONOMETRY
Trigonometric identities
MENSURATION
GEOMETRY
COORDINATE GEOMETRY
CALCULATORS
MATH FOR KIDS
LIFE MATHEMATICS
SYMMETRY
CONVERSIONS
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
OTHER TOPICS 2.3 Differentiabilityap Calculus Definition
Ratio and proportion shortcuts
Converting repeating decimals in to fractions2.3 Differentiabilityap Calculus Notes
SBI!
Download here: http://gg.gg/ojk8z
https://diarynote-jp.indered.space
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