rinku sharma2011
What is Limits in Calculus
What is Limits in Calculus If we take the value of x=2, then f(2) = (2^2 -4)/ (2-2) so, f(2) = 4-4 / 0 f(2) = 0/0, which is a vague . To solve the above function we write, f(x)= (x^2 - 2^2) / (x-2) f(x) = (x+2) (x-2) / (x-2) cancelling x-2 from both numerator and denominator we get, f(x) = (x+2) only when x 2. In such situations, we consider the value of 'x' not exactly equal to 2 but near to 2. If value of x= 1.9, then f(x) = 3.9, which is slightly less than 4, if we start increasing the value of x towards 2, we find that we are approaching towards 4, but not exactly 4. Similarly, if we take the value of 'x' a little higher than 2 and not exactly 2, then the value of f(x) will be a little greater than 4. Thus, we say that lim f(x) = m, only when x-> a, f(x) -> m, which means that the value of f(x) approaches to m when x approaches to a. There are certain fundamental theorems on limits: 1. lim f(x) +g(x) = lim f(x) +lim g(x) x->a x->a x->a 2. lim f(x) - g(x) = lim f(x) - lim g(x) x->a x->a x->a 3. lim c. f(x) = c. lim f(x), where c is any constant value. 4.
What is Limits in Calculus
What is Limits in Calculus If we take the value of x=2, then f(2) = (2^2 -4)/ (2-2) so, f(2) = 4-4 / 0 f(2) = 0/0, which is a vague . To solve the above function we write, f(x)= (x^2 - 2^2) / (x-2) f(x) = (x+2) (x-2) / (x-2) cancelling x-2 from both numerator and denominator we get, f(x) = (x+2) only when x 2. In such situations, we consider the value of 'x' not exactly equal to 2 but near to 2. If value of x= 1.9, then f(x) = 3.9, which is slightly less than 4, if we start increasing the value of x towards 2, we find that we are approaching towards 4, but not exactly 4. Similarly, if we take the value of 'x' a little higher than 2 and not exactly 2, then the value of f(x) will be a little greater than 4. Thus, we say that lim f(x) = m, only when x-> a, f(x) -> m, which means that the value of f(x) approaches to m when x approaches to a. There are certain fundamental theorems on limits: 1. lim f(x) +g(x) = lim f(x) +lim g(x) x->a x->a x->a 2. lim f(x) - g(x) = lim f(x) - lim g(x) x->a x->a x->a 3. lim c. f(x) = c. lim f(x), where c is any constant value. 4.