find the derivative 6x<+2 ln(x), (1 point) Find the derivative with respect to x of h(x)...
Q2- Find the length of the curve y = ln(x2 – 1) for 2 < x < 5.
* if <<1 Let h(x) = { 2 – 22 if i< x < 2 2 - 3 if < > 2 Use the limit definition of derivative to find h'(1) if it exists.
Consider the function f(0) = 2x3 + 6x² – 144x +1 with -6<< < 5 This function has an absolute minimum at the point and an absolute maximum at the point Note: both parts of this answer should be entered as an ordered pair, including the parentheses, such as (5, 11). į < x < 5. Consider the function f(1) = 1 – 2 In(x), The absolute maximum value is and this occurs at x equals The absolute minimum value...
Find the length of the curve 3 v=ln(1 +t), 0< < 2. 1+ Length
(h) Define f : [0, 2] + R by 122 if 0 <<<1 f(x) = { ifl<152 Using the limit definition of the derivative and the sequence definition of the limit prove that f'(1) does not exist.
(1 point) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given the first order IVP y 0, х21 (1) Find the explicit solution on the interval 0 < x < 1 У(х) %3 (2) Find the lim y(x) = х—1 (3) Then find the explicit solution on the interval x 1 У(х) —
(1 point) Find a function of x that is equal to the power series En= n(n + 1)x" = for <x< Hint: Compare to the power series for the second derivative of 1-X (1 point) Find a formula for the sum of the series (n + 1)x" n=0 101+2 for –10 < x < 10. Hint: D,( *) = " " 10n+1
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
T (1 point) Evaluate f(x) dx, where J12) f(x) = { 2.2 -ASX < 0 | 3 sin(x), 0 < x < 1. [fle) de =