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Describe in your own words about the graph where the function becomes
1) Discontinuous at a point.
2) Continuous but not differentiable at a point.
Note: Do not paste graph/images to explain it.
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1) Discontinuous at a point
It means that a function y = f(x) is not defined at some point. Usually such a function possesses vertical asymptotes at such point. If we take the example of a function y = 1/x. We knoe that when x=0, then we get zero in the denominator and division by zero is not allowed, therefore, graph of y = 1/x has discontinuity at x = 0. Also, it possesses a verticle asymptote x = 0.
2) Continuous but not differentiable at a point
Usually such points are of closed shapes e.g. circle, ellipse, etc. etc. Such graphs are continuous at its left most and right most end on the x-axis, but are not differentiable at that point. y = Sqrt(1-x^2) is one such function which is continuous at x = 1 but not differentiable at x = 1.
Calculus Lover gud keep it up
please explain 2nd point ...i dnt understand ..
Thanks..
check the attachment
Please Discuss here about this GDB.Thanks
MTH101 GDB IDEA SOLUTION FALL 2012
MTH101 GDB IDEA SOLUTION FALL 2012
Discontinuous at a point It means that a function y = f(x) is not defined at some point. Usually such a function possesses vertical asymptotes at such point. If we take the example of a function y = 1/x. We know that when x=0, then we get zero in the denominator and division by zero is not allowed, therefore, graph of y = 1/x has discontinuity at x = 0. Also, it possesses a vertical asymptote x = 0. 2) Continuous but not differentiable at a point usually such points are of closed shapes e.g. circle, ellipse, etc. etc. Such graphs are continuous at its left most and right most end on the x-axis, but are not differentiable at that point. y = Sort (1-x^2) is one such function which is continuous at x = 1 but not differentiable at x = 1.
sanasunny gud keep it up
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