How do you find the equation of tangent line to the curve #f(x)=2x^2# at x=1?
Equation of tangent is
Slope of the line is given by value of derivative and as
Hence equation of tangent is
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To find the equation of the tangent line to the curve f(x) = 2x^2 at x = 1, we can follow these steps:
 Find the derivative of the function f(x) with respect to x.
 Evaluate the derivative at x = 1 to find the slope of the tangent line.
 Use the pointslope form of a line, y  y1 = m(x  x1), where (x1, y1) is the point of tangency and m is the slope, to find the equation of the tangent line.
Let's go through these steps:

The derivative of f(x) = 2x^2 can be found using the power rule for differentiation. The power rule states that if f(x) = ax^n, then f'(x) = nax^(n1). Applying this rule, we get f'(x) = 4x.

Evaluating the derivative at x = 1, we have f'(1) = 4(1) = 4. This is the slope of the tangent line.

Now, we can use the pointslope form of a line. Since the point of tangency is (1, f(1)), we need to find the corresponding ycoordinate. Plugging x = 1 into the original function, we get f(1) = 2(1)^2 = 2.
Using the pointslope form with the slope (4) and the point (1, 2), we have y  2 = 4(x  (1)).
Simplifying, we get y  2 = 4(x + 1).
Expanding, we have y  2 = 4x  4.
Finally, rearranging the equation, we get the equation of the tangent line to the curve f(x) = 2x^2 at x = 1 as y = 4x  2.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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