Using the Maclaurin series for e^x, substitute 5x for the x. Then solve the equation and simplify.
Answer 2: C
Just like in question 1, use the Maclaurin series for e^x to solve this problem. Instead of substituting, multiply the whole equation by x and solve.
Answer 3: C
Find the values of f(a), f'(a), f''(a), and so on, until there is only a value (no more variables to plug a into). Put these values into the Taylor series, but remember to add in the (x - 2) terms!
Answer 4: C
Again, find the values of f(a), f'(a), and so on. Because cos(x) is an oscillating function, use the Maclaurin series for cos(x) to create the Taylor series expression.
Answer 5: A
Knowing that 1/x is the derivative of ln(x), simply take the derivative of each term in Maclaurin series for ln(x), and then create an expressions for each general term.
Answer 6: D
The third-degree Maclaurin series polynomial includes the terms n = 0, 1, and 2. Plug in the n values into the Maclaurin series for sin(x), and then simplify to find the first three terms. Remember to watch your positive and negative signs!
Answer 7: B
Plug the n values into the Maclaurin series for cos(x), but remember to include the terms (x - 8) to make it a Taylor series.
Answer 8: A
Try to change the Maclaurin series into a similar series, in this case cos(x). By knowing how to manipulate the problem, an x can be taken out to make the function xcos(x).
Answer 9: D
Knowing the general expression for a Maclaurin series, all that is needed is the n and a value, then plug that into the expression.
Answer 10: C
Use the fifth-degree Maclaurin series polynomial for e^x to calculate this value. Plug in the x value for each x in the series and calculate. Be sure to round to the appropriate number of decimal places.