If y= tanx, x=pi, and dx= .5, what does dy equal?
a)-.25
b) -.5
c) 0
d).5
e).25
if y = tanx
dy/dx = sec^2 x
if dx=.5 and x=π
dy/.5 = sec^2 π , ------ (cosπ = -1, so secπ = -1)
dy = .5(-1)^2 = .5
Well, let's have a little mathematical circus here! If we have y = tanx and we want to find dy, we have to take the derivative. The derivative of tanx is sec^2(x). Now, if x = pi, we can substitute it into the derivative. The derivative becomes sec^2(pi). And since sec(pi) equals -1, we get (-1)^2, which is 1.
But hold your horses, we still need to consider dx. Since dx is 0.5, when we multiply dy = 1 by dx = 0.5, we get 0.5.
So, hooray! The answer is d) 0.5. Keep those math tricks rolling!
To find dy, you need to differentiate y = tan(x) with respect to x. The derivative of tan(x) is sec^2(x). So, dy/dx = sec^2(x).
Since x = pi, we can substitute this value into the derivative:
dy/dx = sec^2(pi)
Now, sec(pi) is equal to -1.
Therefore, dy/dx = (-1)^2 = 1.
Given that dx = 0.5, we can find dy by multiplying dy/dx by dx:
dy = dy/dx * dx
dy = 1 * 0.5
So, dy = 0.5.
Therefore, the answer is (d) 0.5.
To find the value of dy, we can use the derivative of the tangent function, which is sec^2(x).
Given that x = π and dx = 0.5, we can substitute these values into the derivative to find dy.
dy = sec^2(x) * dx = sec^2(π) * 0.5
Now, let's evaluate sec^2(π):
The secant function is the reciprocal of the cosine function, so sec(π) = 1 / cos(π).
cos(π) is equal to -1, so sec(π) = 1 / (-1) = -1.
Now, we can substitute sec^2(π) into the equation for dy:
dy = (-1)^2 * 0.5 = 1 * 0.5 = 0.5
Therefore, dy equals 0.5.
So, the correct answer is (d) 0.5.