How do you find at equation of the tangent line to the graph #y=(cosx)/(sinx+2)# at x =pi/2?
Start by finding the ycoordinate of tangency.
Now differentiate using the quotient rule.
We now find the equation of the tangent.
Hopefully, this helps!
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To find the equation of the tangent line to the graph of y = (cosx)/(sinx+2) at x = pi/2, we can follow these steps:
 Find the derivative of the function y = (cosx)/(sinx+2) using the quotient rule.
 Evaluate the derivative at x = pi/2 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:

Differentiating y = (cosx)/(sinx+2) using the quotient rule:
 The derivative of the numerator, cosx, is sinx.
 The derivative of the denominator, sinx+2, is cosx.
 Applying the quotient rule: (cosx * (sinx+2)  (cosx * cosx)) / (sinx+2)^2.
 Simplifying the numerator: (cosx * sinx + 2cosx  cos^2x) / (sinx+2)^2.

Evaluating the derivative at x = pi/2:
 Substitute x = pi/2 into the derivative expression obtained in step 1.
 Simplifying the expression: (1 * 1 + 2 * 0  cos^2(pi/2)) / (sin(pi/2)+2)^2.
 Since cos(pi/2) = 0 and sin(pi/2) = 1, the expression becomes: (1  0) / (1+2)^2 = 1/9.

Using the pointslope form of a line:
 The point of tangency is (pi/2, (cos(pi/2))/(sin(pi/2)+2)).
 Substituting the values into the pointslope form: y  ((cos(pi/2))/(sin(pi/2)+2)) = (1/9)(x  pi/2).
 Simplifying the equation: y  (1/2) = (1/9)(x  pi/2).
Therefore, the equation of the tangent line to the graph y = (cosx)/(sinx+2) at x = pi/2 is y  (1/2) = (1/9)(x  pi/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.
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