(1 point) For the curve given by r(t) = (2t, 5t, 1 – 5t), Find the derivative r'(t) =( > Find the second derivative p"(t) = ( 1 Find the curvature at t = 1 K(1) =
For f(t) = 3 +5t, For g(t) = 3 - t, find f(1) +g(-2). 1. 8 2. 13 3. 5 4. 3
5. A pebble falls from the top of a cliff that is 180 m high. The pebble's height above the ground is modelled by h(t) -5t-5t+180 where h is the height in metres at t seconds since the pebble started to fall. a. Find the average rate of change between 1 s and 4 s. b. Find h(3) c. Find the instantaneous rate of change of height at 3 s. d. Explain the meaning of each value calculated in parts...
please solve!! Find the Laplace Transform of: g(t) = 1(t-5)·cos(5t-15) 1. Find the Laplace Transform of: g(t) = 1(t-5)·cos(5t-15) 1.
B2. Find the steady-state errors for inputs of 5 u(t), 5t-u(t), and 5t-u(t) to the system shown in the following figure. The function u(t) is the unit step. R(S) + E(S) C($) 120(s + 2) (s + 3)(s +4)
Evaluate the following function at the values t+2 and t+h. 3 g(t) 5t-8t g(t+ 2) (Simplify your answer. Type an expression using t as the variable. For the following function, determine the difference quotient x+h)- f(x) h f(x) 5x-9x fix+h)- fx) h (Simplify your answer. Use integers or fractions for any numbers in the expression.) .Z.O Find the x-intercept(s) and the y-intercept of the function P(x)-3x +22x2 +7x Select the correct choice below and fill in any answer boxes within...
i need help with 3 , 4 and 5 please ... 3.2 The Derivative as a function Q1-Q5. Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. Q1. f(x) = x - Q2. f(t) = 5t - 9t? Q3. f(x) = x3 - 3x + 5 Q4. g(x) = V1 + 2x Q5. G(t) =* 1+1
Let r(t) = <cos(5t), sin(5t), v7t>. (a) (7 points) Find |r'(t)|| (b) (7 points) Find and simplify T(t), the unit tangent vector. Upload Choose a File
(a) Express (∂Cp/∂P)T as a second derivative of H and find its relation to (∂H/∂P)T. (b) From the relationships found in (a), show that (∂Cp/∂V)T=0 for a perfect gas.
QUESTION 5 Find the derivative. + y = In(2x + 1) - e OR T T T Arial V 3 (12pt) T