# At what point on the given curve is the tangent line parallel to the line 5x - y = 5? y = 4 + 2ex − 5x

Equation of given curve:

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To find the point on the given curve where the tangent line is parallel to the line 5x - y = 5, we need to find the derivative of the curve and set it equal to the slope of the given line.

The derivative of y = 4 + 2ex − 5x is dy/dx = 2ex - 5.

The slope of the line 5x - y = 5 can be determined by rearranging the equation to y = 5x - 5, which is in the form y = mx + b, where m represents the slope. Therefore, the slope of the line is 5.

Setting the derivative equal to the slope of the line, we have 2ex - 5 = 5.

Solving this equation for x, we get x = ln(5/2).

To find the corresponding y-coordinate, we substitute this value of x back into the original equation y = 4 + 2ex − 5x.

Therefore, the point on the given curve where the tangent line is parallel to the line 5x - y = 5 is (ln(5/2), 4 + 2e^(ln(5/2)) − 5(ln(5/2))).

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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.

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