Botswana international university of science and technology
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All courses for Botswana international university of science and technology
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Calculus MATH102 10
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Chemistry Chem102 16
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Statistics STATS101 8
Latest notes & summaries Botswana international university of science and technology
If f is a function of x, then the instantaneous rate of change at x=a is the limit of the average rate of change over a short interval, as we make that interval smaller and smaller. ... This is the slope of the line tangent to y=f(x) at the point (a,f(a))
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- • 9 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
Preview 2 out of 9 pages
If f is a function of x, then the instantaneous rate of change at x=a is the limit of the average rate of change over a short interval, as we make that interval smaller and smaller. ... This is the slope of the line tangent to y=f(x) at the point (a,f(a))
A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.
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- • 8 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
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A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.
The limit of a constant times a function is equal to the constant times the limit of the function. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits. The limit of a constant function is equal to the constant.
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- • 11 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781285415376
Preview 2 out of 11 pages
The limit of a constant times a function is equal to the constant times the limit of the function. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits. The limit of a constant function is equal to the constant.
A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1.
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- • 14 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
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A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1.
In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero. ... As x approaches 2 from the left, the numerator approaches 5, and the denominator approaches 0 through negative values; hence, the function decreases without bound and .
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- • 12 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
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In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero. ... As x approaches 2 from the left, the numerator approaches 5, and the denominator approaches 0 through negative values; hence, the function decreases without bound and .
The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
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- • 10 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
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The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Evaluating Limits. Just Put The Value In. The first thing to try is just putting the value of the limit in, and see if it works (in other words substitution). Factors. We can try factoring. Conjugate. Infinite Limits and Rational Functions. L'Hôpital's Rule. Formal Method.
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- • 9 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
Preview 2 out of 9 pages
Evaluating Limits. Just Put The Value In. The first thing to try is just putting the value of the limit in, and see if it works (in other words substitution). Factors. We can try factoring. Conjugate. Infinite Limits and Rational Functions. L'Hôpital's Rule. Formal Method.
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. ... Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.
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- • 8 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781337514507
Preview 2 out of 8 pages
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. ... Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.
Limits at infinity are used to describe the behavior of functions as the independent variable increases or decreases without bound. If a function approaches a numerical value L in either of these situations, write. and f( x) is said to have a horizontal asymptote at y = L.) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point...
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- • 11 pages's •
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Botswana international university of science and technology•Calculus
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Calculus: A Complete Introduction • Hugh Neill• ISBN 9781473678453
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Limits at infinity are used to describe the behavior of functions as the independent variable increases or decreases without bound. If a function approaches a numerical value L in either of these situations, write. and f( x) is said to have a horizontal asymptote at y = L.) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point...
Learn rules of differentiation and derivatives as a function
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- • 13 pages's •
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Botswana international university of science and technology•Calculus
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Calculus • Ron Larson, Bruce H. Edwards• ISBN 9781285415376
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Learn rules of differentiation and derivatives as a function