# AP calculus exam tikx graph of e (tan x ) -2

• MHB
• karush
In summary, the graph of $y=e^{\tan x} - 2$ crosses the x-axis at one point in the interval [0,1] and the slope of the graph at this point is approximately 2.961. This can be calculated by taking the derivative of the function and evaluating it at the intersection point, which is approximately 2.961. This can also be confirmed through graphing and using a calculator. Therefore, the correct answer is D.
karush
Gold Member
MHB
The graph of $y=e^{\tan x} - 2$ crosses the x-axis at one point in the interval [0,1]. What is the slope of the graph at this point.

A. 0.606
B 2
C 2.242
D 2.961
E 3.747ok i tried to do a simple graph of y= with tikx but after an hour trying failed
doing this in demos it seens the answer is D

I know you take the differential set it to zero and that should give you the x value of intersection

karush said:
The graph of $y=e^{\tan x} - 2$ crosses the x-axis at one point in the interval [0,1]. What is the slope of the graph at this point.

A. 0.606
B 2
C 2.242
D 2.961
E 3.747ok i tried to do a simple graph of y= with tikx but after an hour trying failed
doing this in demos it seens the answer is D

I know you take the differential set it to zero and that should give you the x value of intersection ?

AP exams are designed to utilize a hand-held calculator ...

Graph the function within the given interval, calculate the zero and store it a register, then calculate the derivative value at that zero.

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looks like a TI how did you get the screen shots?

My ti84 emulator has a "take screenshot" capability

Observing that $y=e^{\tan x} - 2$ has a root in [0, 1] at $\text{atan}(\log2)$, we need to evaluate $2\sec^2(\text{atan}(\log2))$. That is approximately 2.961, hence choice D is correct.

## 1. What is the purpose of the AP calculus exam?

The AP calculus exam is a standardized test used to assess a student's understanding of basic calculus concepts and their ability to apply them in various problem-solving scenarios. It is typically taken by high school students who wish to earn college credit for their calculus coursework.

## 2. What is the tikx graph of e (tan x ) -2?

The tikx graph of e (tan x ) -2 is a graph of the function e^(tan x) - 2. This function represents the exponential growth of e to the power of the tangent of x, with a horizontal shift of 2 units downward. The graph will have an asymptote at x = π/2 and will approach infinity as x approaches π/2 from either side.

## 3. How is the graph of e (tan x ) -2 related to the unit circle?

The graph of e (tan x ) -2 is related to the unit circle in that it represents the values of the tangent function when multiplied by e and shifted downward by 2 units. The unit circle is a fundamental concept in trigonometry and is used to understand the values of trigonometric functions at different angles.

## 4. What is the significance of the value e in the graph of e (tan x ) -2?

The value e is a mathematical constant that represents the base of the natural logarithm. In the graph of e (tan x ) -2, e is used as the base of the exponential function, which results in a rapidly increasing curve. This value is significant in calculus as it is used in many applications, such as compound interest and population growth.

## 5. How can I prepare for the AP calculus exam?

To prepare for the AP calculus exam, it is important to review all of the concepts covered in your calculus coursework, including derivatives, integrals, and applications of calculus. It is also helpful to practice with past exam questions and to familiarize yourself with the format and timing of the exam. Additionally, seeking help from a teacher or tutor can provide valuable support and guidance in preparing for the exam.

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