![]() As x crosses the value π / 2, tan x becomes negative and is arbitrarily large in magnitude. As x increases from 0 to π/ 2, tan x keeps on increasing from 0 to ∞. We know that tan x is a periodic function with period π This means it repeats itself after each π as we go left to right on the graph. So there will be a "gap" in the function at that point. When this happens, we have 0 in the denominator of the fraction and this means it is undefined. This graph looks like discontinue curve because for certain values tangent is not defined.įor some values of x, cos x has value 0. The slope of a line can be found by calculating “rise over run” or “the change in the y over the change in the x.” The symbol for slope is mĪ tangent line is a line that "just touches" a curve at a single point and no others.Tangent Graph Tangent graph is not like a sine and cosine curve. A line can have positive, negative, zero (horizontal), or undefined (vertical) slope. Slope is a measure of the steepness of a line. The instantaneous rate of change of a curve at a given point is the slope of the line tangent to the curve at that point.Ī secant line is a line that joins two points on a curve. The average rate of change of a function is the change in y coordinates of a function, divided by the change in x coordinates.ĭifferential calculus is the branch of calculus based on finding the difference in location between two points that get closer together until the distance between them is infinitely small. Find the equation of the tangent line to the graph of b(x)=−5x 4+3x 3−x 2+5x−3 at x=−1Ī line that intersects a circle in two points.Ī line that intersects a circle in exactly one point. ![]()
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