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How do you solve to find slope?
The answer depends on the nature of the function that defines the curve whose slope you want. If the function f(x) is differentiable, its slope is f'(x) = df(x)/dx and the value of the slope at a point when x = x0 is f'(x0), obtained by substituting x0 for x in f'(x).
What is X to the 0 power over x to the -5 power?
5
What is the correct procedure for epsilon-delta proofs in Calculus?
A function f(x), of a variable x, is said to have a limiting value of f(xo) as x approaches x0 if, given any value of epsilon, however small, it is possible to find a value delta such that |f(x) - f(x0)| < epsilon for all x such that |x - x0| < delta.The second inequality can be one-sided.
What is the equation of sphere?
The equation of a sphere with radius r, centered at (x0 ,y0 ,z0 ) is (x-x0 )+(y-y0 )+(z-z0 )=r2
How the results of 0x1 2-1 x0?
In order to get the results of 0x1*2-1*x0 you will have to do a little math. The answer to this math problem is X equals one.
Equation for linear approximation?
The general equation for a linear approximation is f(x) ≈ f(x0) + f'(x0)(x-x0) where f(x0) is the value of the function at x0 and f'(x0) is the derivative at x0. This describes a tangent line used to approximate the function. In higher order functions, the same concept can be applied. f(x,y) ≈ f(x0,y0) + fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) where f(x0,y0) is the value of the function at (x0,y0), fx(x0,y0) is the partial derivative with respect to x at (x0,y0), and fy(x0,y0) is the partial derivative with respect to y at (x0,y0). This describes a tangent plane used to approximate a surface.
How do you prove that a to the power of 0 equals 1?
You first define negative powers as the reciprocals of the positive powers ie x-a = 1/xa. You have the folowing property for positive powers: xa * xb = xa+b You extend the following property to negative powers: So xa * x-a = x0. But by definition, xa * x-a = xa * 1/xa = 1 So x0 = 1
How do you solve to find slope?
The answer depends on the nature of the function that defines the curve whose slope you want. If the function f(x) is differentiable, its slope is f'(x) = df(x)/dx and the value of the slope at a point when x = x0 is f'(x0), obtained by substituting x0 for x in f'(x).
What causes the graph of a rational function to have a vertical asymptote?
When your input variable causes your denominator to equal zero. * * * * * A rational function of a variable, x is of the form f(x)/g(x), the ratio of two functions of x. Suppose g(x) has a zero at x = x0. That is, g(x0) = 0. If f(x0) is not also equal to 0 then at x = x0 the rational function would involve division by 0. But division by 0 is not defined. Depending on whether the signs of f(x) and g(x) are the same or different, as x approaches x0 the ratio become increasingly large, or small. These "infinitely" large or small values are the asymptotes of the rational function at x = x0. If f(x0) = 0, you may or may not have an asymptote - depending on the first derivatives of the two functions.
What is X to the 0 power over x to the -5 power?
5
How can you find an equation line between two pair of points?
Assuming you want the equation of the straight line between the two points (x0, y0) and (x1, y1), the equation is: y - y0 = m(x - x0) where m is the gradient between the two points: m = (y1 - y0) ÷ (x1 - x0) Note: if the two x coordinates are equal, that is x0 = x1, then the equation of the line is x = x0.
What is the correct procedure for epsilon-delta proofs in Calculus?
A function f(x), of a variable x, is said to have a limiting value of f(xo) as x approaches x0 if, given any value of epsilon, however small, it is possible to find a value delta such that |f(x) - f(x0)| < epsilon for all x such that |x - x0| < delta.The second inequality can be one-sided.
The square root of -x if x0?
If x is 0, the square root is 0 also.
What is the equation of sphere?
The equation of a sphere with radius r, centered at (x0 ,y0 ,z0 ) is (x-x0 )+(y-y0 )+(z-z0 )=r2
Why does everything to the 0 power 1?
The multiplicative law of indices states that xa * xb = xa+b Now, if you put b = 0 in that equation you get xa * x0 = xa+0 But a+0 = a so the right hand side is simply xa Which means, the equation becomes xa * x0 = xa This is true for any x. That is, multiplying any number by x0 leaves it unchanged. By the identity property of multiplication, there is only one such number and that is 1. So x0 must be 1.
How the results of 0x1 2-1 x0?
In order to get the results of 0x1*2-1*x0 you will have to do a little math. The answer to this math problem is X equals one.
How do you find whether a tangent line is vertical to a function?
A tangent line is NEVER vertical to a function. It is vertical to the normal to the function - which is as far from vertical as you can get!The graph of a function, f(x) can have a tangent at a point. Let's call the point (x0,f(x0)). If f'(x) goes to positive infinity or f'(x) goes to negative infinity as x approaches x0 then f(x) has a vertical tangent at that point.
