If f(x) = 15 1. x f'(x) = 0 t²dt then

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A:

Q: Use any method to evaluate the integral. S- 22 dx (121x² + 1)²

A:

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dy dt dy dt x²…

A: when,

Q: The temperature T = T(x,y) in °C at point (x,y) satisfies Tx(1,8) = 2 and Ty(1,8)= -4. If x=e4t-4 cm…

A: The Rate of change of temperature is given as follows

Q: Show using the epsilon-delta definition of a limit that lim (x² - 4x) = −4. x→2

A:

Q: The Maclaurin series of the function f(x)= can be written as f(x) = Cnth where a few of the…

A:

Q: Consider the systems of differential equations dx dt dy dt = For this system, the smaller eigenvalue…

A: The given system is,The matrix A is,Take the determinant equal to zero.

Q: Suppose a product's revenue function is given by R(g) = -5q² + 900g. Find an expression for the…

A: Product's revenue function is given byR(q)=−5q2+900q.

Q: f(z) 2+3x1x², find f'(5).

A: f(x)=2+3x−4x2, find f′(5).

Q: The volume of a cube is decreasing at a constant rate of 2371 cubic centimeters per minute. At the…

A: The volume of a cube is decreasing at a constant rate of 2371 cubic centimeters per minute. At the…

Q: a 10 foot ladder rests against a vertical wall. if the bottom of the ladder slides away from the…

A: Let the horizontal distance of foot of ladder from the wall be x and vertical distance from top of…

Q: Use the shell method to set up (do not evaluate) an integral that calculates the volume of the solid…

A: Given that the region between graphs of  and  for The graph of the region

Q: XPXV!(*2) U!S l/m O

A:

Q: Find implicitly: dx In(xy²z) + x²z² + 2xy³ = 1

A: The given equation is

Q: 1. State the definition of Continuity in relation to limits. 2. Write the definition of a derivative…

A: (a) State the definition of continuity in relation of limits (b) The definition of derivative…

Q: Evaluate the following definite integral. π -T Select the correct choice below and fill in the…

A:

Q: Consider the function f(x) = 23. Which of the following functions are equal to f(x)? Select all that…

A:

Q: Using either the triangle inequality or the reverse triangle inequality, prove the following: ii)…

A: To prove the statement |2x−3|≤5 when |x−3|≤1, using the triangle inequality. The triangle inequality…

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 14. ay my c₁emx,…

A: The given differential equation is; dy/dx - my = c1emx..

Q: Use partial fractions to find the inverse Laplace transform of the following function. s²-5s s4…

A:

Q: For the following trajectory, find the speed associated with the trajectory and then find the length…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the length of the following two-dimensional curve. r(t)= (3t² -8,41²+2), for 0 st≤1 The arc…

A:

Q: 2. An object weighing 27 pounds is thrown downward with a speed of 2 ft/sec and falls to the ground…

A: weigh of the object = 27 poundsdownward speed = 2ft/sWind resistance = 3% of the square of the…

Q: 1. Solve the equation between 0 and 2, 3 sin²(x) + sin(x) = 1 − 3 sin²(x)

A: We are given the trigonometric equation and need to solve it.

Q: The graph of f' (not f) is given below. At which of the marked values of x is A. f(x) greatest x =…

A:

Q: Determine the derivative of the following function. f'(x) = f(x) = (x7 +19)7

A: Given,

Q: Determine whether the equation is exact. If it is, then solve it. 4t y dy + (4 In y + 9)dt = 0 A.…

A:

Q: For the iterated double integral √I+x³ dx dy ix) dy y=4 x=2 L ( y=0 sketch the region of…

A: I=∫y=0y=4(∫x=yx=21+x3dx)dy

Q: Find the derivative of C(x) = 2¹0 - zº C'(z) = j

A: Given,

Q: for g(x) = ln(1-x^2) and f(x) = sqrt(x + 3), determine the subset of the domain of g on which the…

A: To determine the subset of the domain of g(x)=ln(1−x^2) on which the composition f∘g is…

Q: Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 2²/²/(₁ x + e -x) + ²/² ( 1 = 2/(1 ||

A:

Q: Differentiate. y = In (4x² - 7x+9) y'=0

A: The function is The aim is to find the derivative of the function

Q: a kite 50ft above the ground moves horizontally at 9ft/s; at what rate is the angle between the…

A: A kite 50ft above the ground moves horizontally at 9ft/s. To determine the rate at which the angle…

Q: 28. Using the method of "First Principles" and showing all steps, determine the derivative of the…

A:

Q: 2 Find the volume of the solid whose base is the region enclosed by y = x² 3. The cross sections…

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of F'(x) = F [NOTE: Enter a…

A:

Q: The curve is known as the Folium of Decsartes. In 1638 the famous philosopher, diplomat, soldier and…

A: The given curve equation is

Q: ) Define the domain and range of f(x) where f(x) = sin²(x) – 1

A: The function f(x)=sin^2(x)−1 is defined for all real numbers x because the sine function, sin(x), is…

Q: A particle moves according to a law of motion s = f(t), t ≥ 0,  where t is measured in seconds and s…

A:

Q: Use synthetic division and factor theorem to solve the below equation- -3z³ + 140 – 139z + 38z² = 0

A:

Q: Consider a population p of field mice that grows at a rate proportional to the current population,…

A:

Q: Find the directions in which the function increases and decreases most rapidly at P0. Then, find the…

A:

Q: Find the equation of the line tangent to the graph of f(x) = (In x)4 at x = 3. y= (Type your answer…

A:

Q: Evaluate the following. Give your answer as a fraction, NO DECIMALS. If sint = 3/5 and the terminal…

A: sin⁡t=3/5Terminal point of t is in quadrant II.

Q: If r(t) = cos(lt)i+ sin(1t)j -4tk, compute the tangential and normal components of the acceleration…

A: r(t)=cos(t)i + sin(t)j -4tk

Q: 3. Let a=⟨4,5⟩ and b=⟨3,−4⟩. Show that there are scalars s and t so that ?a+?b=⟨−10,−28⟩

A: Note:-Since you asked multiple questions, according to our policy we can answer only first the…

Q: Determine whether the equation is exact. If it is, then solve it. e'(7y - 4t)dt +(3+7e¹) dy = 0 A.…

A:

Q: Evaluate the integral using the following values. 6 6 ["x³ dx = 320, [°x dx = 16, ["dx = 4 b [kf 6…

A:

Q: Write a definite integral that yields the area of the region. (Do not evaluate the integral.) f(x) =…

A:

Q: 2. Find d [ex (x4 * (x² +1)x] dx ¹]. X

A: