Consider: f(x) = x5 In (x) At which a-value(s) do the local maxima/minima occur? (Hint: Because of In x, the domain of function f is x > 0.) (Answers must be exact one. No decimal number! Multiple answers must be separated with a semi-colon ";".) X =

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: Values we also know cos B 1. Suppose we know sin a = and 0 < a < 2, and suppose 2√5 and 5 2 - <3 <…

A:

Q: Suppose that f(x, y) = x² - xy + y² - 4x + 4y, with domain D constrained by the lines y = x, y = 0,…

A: Given function:- fx,y=x2-xy+y2-4x+4y

Q: tangent line

A:

Q: Find the exact value of each of the remaining trigonometric functions of 0. 24 25' sin 9= 90°…

A:

Q: How would I draw the following ellipsoids? 9x^2 + y^2 + z^2 = 9 9x^2 + 4y^2 + 36z^2 = 36

A:

Q: Suppose that u and v are vectors of lengths 1 and 2, respectively. If the angle between u and vis…

A:

Q: Homogeneous DE M(x,y)dx + N(x,y)dy = 0 is Homogeneous if both M and N are homogeneous functions of…

A: Here we have to solve the differential equation.

Q: Let f(x) = X Use logarithmic differentiation to determine the derivative. ƒ'(x) = ƒ'(1) = 8x

A:

Q: Find the local maxima, local minima, and saddle points, if any, for the function z = 2x² + 3y² - 16x…

A:

Q: Given Cost and Revenue functions C(q)=q3−9q2+57q+5000 and R(q)=−3q2+2600q​, what is the marginal…

A: Given Cost and Revenue functions:- Cq=q3-9q2+57q+5000 Rq=-2q2+600q

Q: Consider the following. Find f'(x). f'(x) = f(x) = - Find f'(-1). f'(-1) = 3,2 2 equation y = + 9x +…

A:

Q: dx Assume that x = x(t) and y = y(t). Let y = x³ +6 and=5 when x = 1. dt dy Find when x = 1. dt dy…

A: y=x3+6given  dxdt=5when x=1dxndx=nxn-1

Q: find the absolute maximum and absolute minimum of the function x - 2cosx  on the interval of (-2, 0)

A: we can find the absolute maximum and minimum .

Q: Differentiate f(t) = esin(πt) Answer: f'(t) =

A: Please refer to the image below

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A:

Q: Homogeneous DE M(x,y)dx + N(x,y)dy = 0 is Homogeneous if both M and N are homogeneous functions of…

A: Here we have to solve the differential equation.

Q: Using Identities to Solve Equations 1. Write the function f(a) = sin(3a) - √3 cos(3a) using a single…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Let ƒ'(x) = f¹(e³) = ƒ(x) = (ln x)8

A: f(x)=(lnx)8 d dx(lnx)=1xd dx(xn)=nxn-1lne=1

Q: 10) (1 + √√3) x + (1 -√√3) y = −18 and √√3 x + y = -17

A: Given query is to find the angle between the lines.

Q: vertical cylinder is leaking water at a rate of 1m3/sec. If the cylinder has a height of 10m and a…

A: In a vertical cylinder water is leaking at a rate of 1 m3/sec. dVdt=-1 m3sec Height of the cylinder…

Q: Q6.1 Find an equation of the tangent line to the curve at the point (1, 2). Show all your work. x³y…

A:

Q: S 1 √²-20x+104 dx = +C

A:

Q: Determine the derivatives, dy a.y = log3 (7) → da b.y = ln (2³) dy → c. y = In (7x) → d.y= log3 (2)…

A:

Q: Differentiate the following function with respect to x: (3x² + 5x + 5)5 Submit Assignment Quit

A:

Q: The functions f and g are defined as f(x) = 8x + 5 and g(x) = 10 - 9x. The domain off-g is (Type…

A:

Q: 2.1, #17: For the graph of g given, arrange the following numbers in increasing order and explain…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Find dy da dy da if 9 y² = -5 2² - 10.

A:

Q: Find o implicitly. dx 3x² + xy² +2=0

A: 3x2+xy2+2=0d dx(xm)=mxm-1d dx(u.v)=udvdx+vdudx

Q: Determine dy if y=2e +3 da dy da = HP

A:

Q: Find dy/dx by implicit differentiation. cot(y) = 5x - 8y dy/dx =

A:

Q: If the tangent line to the curve y = f(x) at (4, 3) passes through the point (0, 2), find f (4)

A: If the tangent line to the curve y=fx at 4, 3 passes  through the point 0, 2, then to find f4.

Q: Determine the point(s) on the surface z = xy + 5 + (Give your answer as a comma-separated list of…

A:

Q: Identify the location and value of any relative maxima or minima of the function. If there is more…

A:

Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 9…

A: Given: r(t) = 9 cos(t) i + 8 sin(t)j

Q: Find the derivative of y with respect to x. y=csc¹(x¹²+1), x>0 dx (Type an exact answer, using…

A: Given query is find the derivative.

Q: experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Find…

A: We need to find probability.

Q: Determine the value of dy/dt at x = 2 when 3x² - 5x and dr/dt = 2. y = 1. 2. 3. dy dtx=2 dy dt=2 4.…

A: The given function y=3x2-5x. We have to find the value of dydt at x=2 and dxdt=2.

Q: Find the average value of f on [0, 16]. fave 11 YA 1 0 4 8 12 AX

A: see below the answer and calculation

Q: (a) Solve the following; 2. e¹x14e²x +48=0

A:

Q: Differentiate the function. f(x) = 5x ln(2x) − 5x

A: Given query is to find derivative.

Q: Compute the curl of the vector field F=7z i +4y j +6x k. Curl =   ?

A:

Q: √(√x² - 153) dx 4x3

A:

Q: Please find the requested derivative of the following functions. s²-4st+t² = 4, find 25 ds dt - ds…

A:

Q: Find the length of the curve. r(t) = (st 3 co

A:

Q: ) Determine the equation of the tangent line to the circle 2 -² + y² = 169 at the point (5,12)

A:

Q: Find the complex a) -8 b) 8 + 4i conjugate of c) -4i d) 2e-i/5

A: a) -8 b) 8+4i c) -4i d) 2e-i/5.

Q: 3. Evaluate these integrals. 4 (a) ₁4.2³ 4x3 + da x S 3 sin(2x) dx :) fe*(1-26²)³ de

A: The given integrals, a) ∫144x3+4xdx. b) ∫π4π23sin2xdx c) ∫ex1-2ex3dx. We have to solve each of the…

Q: Let f(x)=2x-9 and g(x)=-(1)/(3)f(-x). identify its x and y-intercept s of f(x)

A: The function is given by fx = 2x-9 gx = -13f-x To determine: The x- and y-intercepts of the function…

Q: Find the derivative of the function by using the rules of differentiation. 9 f(x) = − 1² (x−⁹ — x¹8)…

A: here we have to find the derivative of the function.