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slope predictor formula of tangent line and limits
Given f(x) = (x -4) /(x^2 - 16), find all points where f is not defined (and therefore not continuous). For each point, tell whether or not the discontinuity is removable.
11.
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Continuity and limits of functions
.) (-∞, 9) (9, ∞)Question 10 Figure 10.1 f(x) = x-4 x2-16
Given Figure 10.1, find all points where f is not defined (and therefore not continuous).
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Solving Inequalities, Limits and Derivatives
A straight line is tangent to a given curve at a point on the curve if the line passes through the point on the curve and has slope , where is the derivative of . This line is called a tangent line, or sometimes simply a tangent.
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Find the derivative f 'of f and tangent line
456914 Find the derivative f 'of f and tangent line Let f(x) = x2 + 4x.
(a) Find the derivative f 'of f.
(b) Find the point on the graph of f where the tangent line to the curve is horizontal.
Hint: Find the value of x for which f '(x) = 0.
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derivative and the slope of a curve
Note: We assumed during this judgement that the function f(x) is not only continuous, but differentiable too, which means that its derivatives exist all over on the given domain.
b) Definite integral and area under a curve.
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Tangent lines
252817 Tangent Lines: Example Problem Find an equation for the tangent line at the given curve at the point where x=x0;
a. y=(x^2+3x-1)(2-x); x0=1
b. y=x+7/5-2x; x0;=0
Find all points on the given graph of the given function where the tangent line
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Finding the domain and range of discontinuous functions
To find the points of discontinuity, we need to equate the denominator to zero.
(x-1)(x-2) = 0.
Therefore, x = 1 and x = 2
So the x coordinates of the points are 1 and 2. Therefore, the function is discontinuous at x = 1and x = 2.
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Calculus for Parallel Lines of Graphs
f(x)=4x^2+ 5x+ 2
Find all points "x" where the function whose graph is shown below is discontinuous.
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number ɛ is given.
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Horizontal and vertical line on a polar curve
388593 Horizontal and vertical line on a polar curve Find the points on the given curve where the tangent line is horizontal.
Find the points on the given curve where the tangent line is vertical.
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Astroids and Tangent Lines
According to the point-slope form, the equation of the tangent line is
At the two points and , the slope of the tangent line is . So we can say that the tangent lines are not defined at the two points. An astroid is investigated.