If a population is distributed normally with mean 0 and standard deviation 1, then the probability that a sample will fall within s standard deviations of the mean is S 1 ,-x²/2 dx. Unfortunately, integration techniques you learned in single-variable calculus will not help you take the antiderivative of e-**12. Fortunately, we can approximate this definite integral by replacing f(x) = e-**12 with one of its polynomial approximations. (a) Let f(x) = e-x-12. Find f' (x) and f" (x). Factor e x²/2 out of each answer. (b) Write down the linear and quadratic approximations for f(x) at 0. (c) Use Taylor's formula to find an error bound for your linear approximation that is valid on the interval (-, ). (Hint: f(2) is a product of terms. To find a bound for 2? f(2), start by finding a bound for each factor.)

Q: Choose True if the statement is correct, otherwise False. If an integration process produces a…

A: If an integration process produces a constant number, it cannot be added with the constant of…

Q: If f(x) = x + VT, find f' (1)

A:

Q: Given f''(x)=9x^3-5x^2+10x-8,f'(1)=1 and f(1)=2 Find f'(x) and f(x). part 1: Find the antiderative…

A:

Q: If f(x) = (3x +8) find f'(z). Find f'(1).

A:

Q: if y= (1+e^x)X^3 then find y`

A:

Q: If x = t^2 + 1 and y = t^3, then the second derivative is? (Show your complete solution). a. 3/(4t)…

A: Given that,   x=t2+1 and y=t3

Q: If f(x)=(x^2+5x+2)^2 find f'(x) and f'(3).

A: The given function is: f(x)=x2+5x+22

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: Why is e^x^3 using the product rule instead of the chain rule??

A:

Q: The rate of spending (in billions of dollars per year) on research and development (R&D) in the…

A:

Q: 2x + 3 f(x) = In %3D 7r – 7 f'(x) =

A:

Q: If f(x)=7−x^2/6+x^2 find f'(x)

A: The function is given by fx = 7-x26+x2 To evaluate:The expression of f'x

Q: The integrating factor of the non exact DE ydx-xdy=- is -1/x^2, show your solution

A: We have to find

Q: The percentage of the US population with diabetes is D(x)=0.96+0.011e^x+lnx where x is the number of…

A: The function that models the percentage of US population with diabetes is, Dx=0.96+0.011ex+lnx Here…

Q: 1 64 + 4f(1) + 7z²(f(x))* = 0 and f(1) = -2, find f'(1).

A: Given:

Q: please differentiate the function

A:

Q: Given f''(x) = 5x + 1 and f'( – 1) = - 5 and f( – 1) = 4. %3D Find f'(x) = and find f(2) Preview…

A:

Q: If f(x) = x2 - Vx + 2, find f'(x). %3D f'(x) = %3D

A:

Q: if f(x)=(x^2+4x+2)^2 find f'(x) and f'(1)

A:

Q: The Integrating factor is wrong, look back at question and notice that 1/x is wrong, it is supposed…

A:

Q: Find f. f(x) = f'(x) = 24x² + 2x +4, f(1) =1, f(1) = −4

A:

Q: If f(x)= e^(x^2), find f'(x). Could you please show me the steps on how to solve this integral.…

A: Topic = Derivative Using the formula ddxhxgx=h'xgx. g'xddxex=exddxxn=n xn-1