Find the area of the surface. The portion of the plane z = 6 - 3x - 2y in the first octant 6√14

Q: 5. Evaluate the definite integrals, using the Fundamental Theorem of Calculus to find an exact…

A: To evaluate the definite integrals, by using the Fundamental Theorem of Calculus to find an exact…

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

A:

Q: Evaluate the integral using Substition method dx 3 STAC X (1+√x) ²

A:

Q: Draw and label a diagram to help solve the related-rates problem. The side of a cube increases at a…

A: We consider a cube on each side is x m long.Draw a cube and mark its length, width and height as x m…

Q: For the graph of a function y = f(x) shown to the right, find the absolute maximum and the absolute…

A:

Q: Suppose the amount of caffeine (in mg) in a person's body t hours after consuming it is C(t) = 75…

A: Suppose the amount of caffeine (in mg) in a person's body t hours after consuming it isTo compute…

Q: Sketch the situation if necessary and use related rates to solve. A 6 ft tall person walks away from…

A:

Q: Intervals of Increase and Decrease and Local Extrema Answer the following questions using the…

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

Q: Using the given graph of the function f, find the following. (a) the intercepts, if any (b) its…

A:

Q: Find dy/dx by implicit differentiation. ex/y = 9x - y y (9y-¹) y²-xexv Enhanced Feedback

A:

Q: = x - 8.

A:

Q: Select all of the following for which there exist nonzero constants which can be substituted into…

A: We take each equation and compare of both sides to solve for a, b and c. If the values of a,b and c…

Q: A baseball diamond is a square of side 90 ft. A baseball player runs from a home plate toward the…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(3) and G'(3). F'(3) G'(3) = = f(3) =…

A: Given,  F(x)=f(f(x)) and .Given, f(3)=9, f(9)=3, f'(9)=4, f'(3)=15

Q: If ƒ"(x) = x²(x − 3)(x + 5)³ then ƒ(x) has a point of inflection at Select one: a. x = -5₂ x = 0 and…

A: given

Q: Find how much money needs to be deposited now into an account to obtain $3,900 in 15 years if the…

A: Final Amount, A=$3900Time, t=15 yearsRate of Interest, r= 6.5% per year=0.065

Q: Find the first partial derivatives of the following function. fx: 11 2 2 f(x,y)=√√5x² + 8xy + y² (5x…

A: Given function is as follows

Q: (a) Show using the product rule that [f(x) g(x)h(x)]' = f'(x)g(x)h(x) + f(x)g (x)h(x) +…

A: we are given a product of three functions and we need to find out the derivative using the product…

Q: Find the domain and all critical points in the domain of y = 1- x² is help (intervals) a. Domain of…

A:

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A:

Q: Inverse Laplace transforms can be found using the linearity property of transforms and a reference…

A: The linearity property of Inverse Laplace Transform:Where  and  is the constant.And the Inverse…

Q: Differentiate f(x) = tan¯¹(x³). Answer: f'(x) =

A:

Q: Jse the graph of h (x) below to evaluate lim_h (x), if possible. x→2 4

A:

Q: If x² + y² + z² = 9, dz dt dx dt X dy = 4, and dt dz = 6, find dt when (x, y, z)= (2, 2, 1).

A:

Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. L(x) = f(x) = sin(x), a…

A: L(x) =f(a)+f'(a)(x-a) .

Q: For the formula Dûƒ(P) = Vƒ(P) · û to hold, what must be true of û?

A:

Q: Find an equation of the tangent line to the curve at the point (1, 1). y = x^e-x y =

A: to find the tangent line at (1,1/e) to the curve y=(x^4)(e^(-x))

Q: Find the solution of the differential equation that satisfies the given initial condition. du dt =…

A: Consider the differential equation

Q: Evaluate the integral using the following values. 8 8 8 [³x³ dx = 1,020, [²x dx = 30, [° dx = 6 8…

A: Given that the value of the some integral  and we evaluate the value of other integral by using…

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

A: Given:To Find:(a) Find the rate of change of the brightness after t days.(b) Find, correct to two…

Q: (c) Does the volume of the cylinder of part (b) increase or decrease as t increases? (a) Find V'(t).…

A:

Q: 1. Find the derivative for each of the following functions. You need not simplify your answers. ex…

A:

Q: Approximate cos(1.5) using a quadratic approximation:  First note that cos(1.5) ≈ cos(pi/2). Let…

A: To approximate cos(1.5) using a quadratic approximation.

Q: Find the derivative of the function. y = sin¯¹(cos¹(t)) y' =

A: Given that expression we have to find the value of

Q: True or false and why? Explain. The linearization of f(x,y) = 5 + 7x + 3y at any point (a,b) is the…

A: To determine whether the following statement is true or false.The linearization of at any point is…

Q: The limit lim g(4+h)-g(4) h is equivalent to: (i) The derivative of g(-x) at x = -4 (ii) The…

A:

Q: 4. Give the phase shift, vertical displacement, amplitude, and period of the following function: ==…

A: To give the phase shift, vertical displacement, amplitude, and period of the following function.

Q: Let g(¹) – (61 – In 1)³. Then g'(x) =

A:

Q: Calculate cos(u) for the following choices of u(x): u(x) = 1 − x², cos(u(x)) = u(x) = x¯6,…

A:

Q: If xy + 5e = 5e, find the value of y" at the point where x = 0. 7 +5e 25e² y" =

A:

Q: The pressure P and volume V of an expanding gas are related by the formula PVb = C, where b and C…

A: Product rule of differentiation:

Q: Use the formula above to determine how long it will take an initial investment of $6,750 to grow to…

A: given here initial investment is $6750 and 10.08% interest rate per year and it is compounded…

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: The figure Let y be the height of the balloon (in km) , t be time (in minutes) and  the angle…

Q: -1 2. Now, compute the antiderivative of (sin cos 0) instead using a trig. identity for sin(20) and…

A:

Q: 23. Time-lagged flights An airliner passes over an airport at noon traveling 500 mi/hr due west. At…

A: SolutionAssume that x is the distance the west bound airliner has travelled between noon and t hours…

Q: A calculator may be used for the following question. Let f(x) be a function such that sinx…

A: given first derivative of function

Q: A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x…

A: We first find the profit function.

Q: Given the following vectors, à = [1, 2, 3] [ [-5, 0, 12] = [2, b = -5, -5]

A:

Q: Use logarithmic differentiation to find the derivative of the function. cos(x) y = sin(x)

A: