Let f(x) be a function defined for x> 0 with (In(x))² f(e) = 6 and f'(x) = = X a. Write the equation of the tangent line of f(x) at the point x-e. b. Is f(x) concave up or down in the interval (1,4)? Please justify your answer. c. Find f(x) by using anti-differentiation.

Q: For f(x) = x² − 6x² + 9x, Find Local Maximum, Local Minimum, and Point of Inflection. {Your answer…

A: For , to find local maximum, local minimum, and pointof inflection.

Q: Find the first partial derivatives of 2x 4y f(x,y) 2x +4y af ?x af ду = (1,3): = (1, 3) = - at the…

A: The two variable function is given by:We need to find the first derivatives at the point Important…

Q: A schematic drawing of a 70-ft dome used by a weather service to house radar is shown to the right.…

A: from figure ,Let AB=yBC=xand AC=35 ft.

Q: Directions: Determine if the given function is a solution of the following initial value problem.…

A: To determine whether the given function is a solution of the followinginitial value…

Q: Find the area between y = sinx and y = cos x on the interval [0, π]. EL YA 2+ f(x) = sin x R₁ R₂ AT…

A:

Q: the

A:

Q: Directions: Find all points (x, y) where f(x, y) has a possible relative maximum, minimum, or saddle…

A: To find all points  has a possible relative maximum, minimum, or a saddle point.

Q: do b and c.......

A: The given differential equation b)  , c) ,

Q: Assume A population of tigers in a reserve grows according to the logistic differential equation.…

A:

Q: Evaluate the indefinite integral. (use C for the constant of integration.) x² √ (2³-36 dz - = 3)8

A:

Q: What is one third of 325?

A:

Q: calculate d and e with good working outs ...

A: To solve the following first order linear differential equation, is given by

Q: a) Solve Cauchy problem for the non-homogeneous ovo andhulsel) aogel botning (som equation: Elo…

A:

Q: If you know that f(x) = f"(x) and that f(-6)= 7 while f(-2) = 7e^4 then: integral -6 - 2x*f"(x) dx =…

A: f(x)= f"(x) f(-6)=7 f(-2)=7e4 We have to find ∫(-6-2xf"(x))dx

Q: Evaluate the limit lim Select one: 2 a. O b. O c. - e. 23x-30 *+10+ x²-100 20 7 10 O d. does not…

A: Need to find out the limit by using the L-hospital rule.

Q: J Inxdx.

A:

Q: Arik works the following hours during a one-week period: Hours 7 8 Day Monday Tuesday Wednesday…

A:

Q: Let a be a nonzero real number. For any xo satisfying 0 < x < 2/a, the recursive sequence defined by…

A: The objective of this question is to find the limiting value, order of convergence, and the…

Q: Evaluate the limit exactly. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the…

A:

Q: Estimate the slope of the tangent line of the function f(x) = 7e* at the point x = e. (Use decimal…

A:

Q: 2. A manufacturer wants to design an open box having a square base and a surface area of 104 square…

A:

Q: 1. Solve the inequality 2x² -8 <0.

A: Consider the inequality

Q: Find the general solution to the differential equation 4d² y + y + d x² 36dy - 4y=8sin2x dx

A:

Q: 20) Find the conditions on a and d such that the matrix A = [] has and inverse. What is the inverse…

A: Given,

Q: Evaluate the following limits. If necessary, enter INF for ∞ and -INF for -∞. a) lim →∞0 b) lim 4 60…

A:

Q: S₁²+ x² + 12x +35 Select one: O a. Inx+5 +1n|x +7 |+C O b. In|x+51 In x+7| (In)x+ 5 )(lnx + 7) + C…

A:

Q: Question 3 Find the limit, if it exists. If it does not, enter "DNE 2x³ - 6x-4 4x² + x lim x→→∞

A:

Q: Find the area of the parallelogram whose vertices are given. A(0,0,0), B(3,2,6), C(4,1,6), D(1,-1,0)…

A: Area of parallelogram is given by

Q: 1. Solve the system of equations algebraically: y = 2x² - 4x+5 x² +2=y

A: The given equations are: y=2x2-4x+5 y= x2+2

Q: how do i find the tension in ropes at angles of 35 degrees and 50 degrres holding a load of 800…

A: The objective of this question is to find the tension in two ropes holding a load of 800 pounds at…

Q: Suppose that the total cost function, in dollars, for the production of x units of a product is…

A: Cost function for the production of x units is : Average cost of producing x items is :

Q: Choose the graph that depicts a one-to-one function. O O 4 S o T O

A:

Q: Use the graph below to determine the limits. lim f(x) x-1 lim f(x) x-2 lim f(x) x-3 y=f(x) lim f(x)

A:

Q: Given the function y = 4x² - 4: a. To find the arclength from=0 to x = 5, which is the correct…

A:

Q: Consider the following. (b) x-6, f(x) = x² + 1, 7-X₁ Find each limit. (If the limit is infinite,…

A:

Q: Directions: Calculate the following indefinite integral (make sure you include +C as part of your…

A: Let,

Q: Directions: Both first partial derivatives of the function f(x, y) are zero at each of the given…

A:

Q: (b) ∞ 2 X 2 2 (8x² - 12x) dx -∞

A: given integration

Q: Calculate the following iterated integral. L (L xydy) dx =

A:

Q: -) = (3x² + 6xy²) + (6x³y + 4y³)] ) is conservative. calar potential for F(x,y) is y² + y² + x³ + k.

A:

Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

A:

Q: = Consider the function f(x) = 100 x +² , x < 0. Determine the local extreme point 4

A: f(x)= 100/x + x/4

Q: The graph of f (x) is shown below. Find: f(x)dx 1 1 -1. G www ... 13 10 ........ f(2 40

A:

Q: x-5 x³+x² dx

A: To evaluate the following integral.

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: The given function is, From the Intermediate value theorem,  if  is a continuous function over a…

Q: Find the horizontal and vertical asymptotes of f(x). f(x) = 6 X 2 x + 2 Find the horizontal…

A:

Q: c) Solve Cauchy problem: y" - 4y' + 5y = 0, y(0) = 1, y'(0) = 0

A: Given that here need to find the solution of the given differential equationby Cauchy -Euler method…

Q: Find the values of the logarithms for the given conditions. Each response should be entered as: • a…

A:

Q: 21. Consider the function y = 2* + 3. a) Find the (i) y-intercept (ii) equation of the asymptote b)…

A:

Q: Directions: Calculate the following definite integral. Use the substitution rule or integration by…

A: