Calculus

Botswana international university of science and technology

Here are the best resources to pass Calculus. Find Calculus study guides, notes, assignments, and much more.

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Limits(rate of change & instanteous velocity) Limits(rate of change & instanteous velocity)
  • Limits(rate of change & instanteous velocity)

  • Class notes • 9 pages • 2020
  • 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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Limits of functions Limits of functions
  • Limits of functions

  • Class notes • 8 pages • 2020
  • 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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Limit laws Limit laws
  • Limit laws

  • Class notes • 11 pages • 2020
  • 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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Limits by algebric manipulation and one sided limits Limits by algebric manipulation and one sided limits
  • Limits by algebric manipulation and one sided limits

  • Class notes • 14 pages • 2020
  • 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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Infinite limits Infinite limits
  • Infinite limits

  • Class notes • 12 pages • 2020
  • 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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Differentiation Differentiation
  • Differentiation

  • Class notes • 10 pages • 2020
  • 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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Finding limits by evaluation Finding limits by evaluation
  • Finding limits by evaluation

  • Class notes • 9 pages • 2020
  • 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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Continuity and Discontinuity Continuity and Discontinuity
  • Continuity and Discontinuity

  • Class notes • 8 pages • 2020
  • 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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Limits at infinity and Tangent lines Limits at infinity and Tangent lines
  • Limits at infinity and Tangent lines

  • Class notes • 11 pages • 2020
  • 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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Derivative as a function Derivative as a function
  • Derivative as a function

  • Summary • 13 pages • 2020
  • Learn rules of differentiation and derivatives as a function
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