1:) What is the area enclosed by the graphs of the equations y = 2x − x^2 and y = −3?
2:) What is the derivative of the function
1:) What is the area enclosed by the graphs of the equations y = 2x − x^2 and y = −3? 2:) What is the derivative of the function - csc(t)dt - csc(t)dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
-1 CSC х The derivative of the function y at a 1 is equal to I Select one: a. -1 b. Does not exist e c. O d. 1 The derivative of the function e5z - In z is equal to Select one: e5z-In 1 5 b.e х C. e5z-In z -5 d. e5z-Inz T
QUESTION 6 Find the area enclosed by the x-axis and the curve x=4+3, y=t-7 O a. 44 + 3t dt 404 + 3t dt 06.261 -2534 -25%A4+31 Oc 125e - eat O d. 12/²3 - eat
The area of the region enclosed by the curves y = 2x, 3y = X and 2y = -x+5 is none of these o o 3,5 0 2.5 0 o o
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
2) Find the area of the region enclosed by each group of equations. a) y x, y sin x, b) y x2-2x, y= x+ 4 x 3) A particle moves along a straight line with a velocity of 5 cm/s and then accelerates at a rate of a(t) t2+2. What is its displacement after 5 seconds of acceleration (acceleration is in cm/s2) 4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially...
Solve the given system of differential equations by systematic elimination. dx dt = 2x − y dy dt = x (x(t), y(t)) =
Find the area of the region bounded by the graphs of the equations. y = 8x2 + 4, x = 0, x = 2, y = 0 Evaluate the definite integral by the limit definition. 7 x dx -6 X Evaluate the definite integral. Use a graphing utility to verify your result. (t1/ dt
9. (a) Let Ao(x) = / (1-t*)dt, Ai(z) = / (1-t2) dt, and A2(z) = / (1-t2)dt. Compute these explicitly in terms ofェusing Part 2 of the Fundamental Theorem of Calculus. b) Over the interval [0,2], use your answers in part (a) to sketch the graphs of y Ao(x), y A1(x), and y A2(x) on the same set of axes. (c) How are the three graphs in part (a) related to each other? In particular, what does Part 1 of...