What is the equation of the line tangent to #f(x)=(2x^2 - 1) / x# at #x=1#?
y = 3x -2
Find the equation in slope-intercept form y = mx + c ,where m represents the gradient and c , the y-intercept. We require to find m and c. The value of f'(1) is the gradient of the tangent m , and f(1) will enable us to find c.
Begin by simplifying f(x). Divide terms on numerator by x.
hence partial equation is : y = 3x + c
substitute x = 1 , y = 1 into partial equation to find c.
1 = 3(1) + c → c = -2
and equation of tangent at x = 1 is y = 3x -2 graph{(y-((2x^2-1)/x))(y-3x+2)=0 [-10, 10, -5, 5]}
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The equation of the line tangent to f(x)=(2x^2 - 1) / x at x=1 is y = 3x - 1.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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