What are the vertices of the hyperbola whose equation is: * 9x² -4y² +72x + 108 = 0 (-1,0) and (-7,0) O(-4, 2) and (-4,-2) O(-2,0) and (-6,0) O(-4,3) and (-4,-3)

Q: State whether L'Hôpital's Rule applies or not. x² - 25 lim x-5 54x - x² Does L'Hôpital's Rule apply?…

A: We have to check weather the L'Hospital rule is applicable or not after that we have to calculate…

Q: (a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of…

A:

Q: Find the transition points. y = 2x^ = 18x* (Use symbolic notation and fractions where needed. Give…

A:

Q: Is it possible to Solve all the points with Finding Domain and Range y= sin x 2) y = cos x 3) tan y…

A:

Q: What is the surface area of the solid generated by revolving about the y-axis, y = 1-², on the…

A: Given

Q: Find the average rate of change of the function over the given interval. f(t) = 13+ sint a. 0, 플] п…

A: As we know that; The average rate of change between the interval t1≤t≤t2 is given by: Average rate…

Q: Obtain the output for t = 1.22, for the differential equation 2y"(t) + 27y(t) = et + et :y(0) = 0,…

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: -1 position (s, cm) 153 10- 5+ 0 2 3 4 time (t, seconds) 5

A: Slope of position(s) graph gives speed. i.e. Speed =dsdt

Q: S 10dz 4z³-4z² + 5z

A:

Q: Find all the relative extreme values in the domain of y = tan(x)

A: Find all the relative extreme values in the domain of y = tan(x)

Q: The graph of a function y = f (x) is shown below. Use the graph to estimate all (there may be more…

A:

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

Q: find area between line y=-2+x and y=x^(1/2) and x-axis 26/4 O 23/6 O 36/2 O

A: Here we have given equations of two lines as  : y=x and y=x-2.

Q: S tan |2x dx Evaluate

A:

Q: 4 Consider the force field Ğ(x, y, z) = = = -ze²y-x, 2ze²y-x, e²y-x 2² + 2x + 2 a. Determine whether…

A:

Q: Find the point (if it exists) at which the following plane and line intersect. - 10x-3y-9z= - 19 and…

A:

Q: in how many ways can we arrange the integers 1, 2, 3, 4, 5 in a line so that there are no occurence…

A: We use the principal of inclusion and exclusion.  For i∈1,2,3,4, let Ai ⊂Si be the set of all…

Q: Consider the circular helix with equation R(t) = (12t, 5 cost, -5 sint). (a) Find the value of t…

A:

Q: Question 2 What is the slope of the tangent line to the graph of x² - xy - 4y² + 2x + 4y = 8 at (4,…

A:

Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

A:

Q: Evaluate the characteristic w "+k²x ²³w = 0 value of k in the following differential equation w…

A:

Q: explain using a graph of (x) = X³-6x, for 0≤x≤3 With Six sub intervals, what the Riemann sum…

A:

Q: Determine if the series converges or diverges Sum n=1 (n+1)/(n+3) State the test used, show that all…

A:

Q: 3 1 L ₁₂x²²49dx +9 -3 RE

A: We have to find value of given Integral.

Q: example I= 1 5² die fex2=212 9=0₁6=1

A: The integration of the integral is x2 limit from 0 to 1.

Q: Determine if 1781 is divisible by 3, 6, 7, 8, and 9.

A: Determine if 1781 is divisible by 3, 6, 7, 8, and 9

Q: Determine whether the following function is differentiable at x = 9 f(x)=√x²-16, x<9 √x, x ≥9 (a)…

A:

Q: B. False 4. Which of the following points is not the point of discontinuity of x-7 f(x)= - ?…

A: Given problem:- Which of the following points is not the point of discontinuity of f(x)= (x-7) /(x3…

Q: dx 9-x

A:

Q: Consider the following double integral 1= dy dx. By reversing the order of integration of I, we…

A:

Q: solve the differential equation 2) 2x² dy dx csc (X)

A:

Q: Find the derivative of the function. - 5x - 4 e to y=xe dy dx ||

A: Finding the derivative of the function

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

A:

Q: For the F(x) function shown in the figure, find P(0≤x≤0.5) F(x) 1 1 2 1 2 1 X

A:

Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

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

Q: Laplace transform of the following functions a) cos3t b) (e^(2t)-e^(-2t))^2

A: Let's solve laplace transform of given function.

Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: X=2Seco y = 4 tano find cay dx² 1. when 0-1

A:

Q: If f(x) = x'ex, find f'(x) and f'(1).

A:

Q: 1. Solve the following equations: c) (x² - 4xy – 2y²) dx + (y² + 4xy – 2x²) dy = 0 -

A: Given :x2-4xy-2y2dx+y2-4xy-2x2dy=0

Q: The marginal cost function in a company is given by C' = 70 - 0.7x where x is the number of units…

A: Please see the below picture for detailed solution.

Q: 2. Evaluate: S 0 trư √2 = x + x dx

A:

Q: Finding the rate of change of the function defined by y = x³ and evaluating it at x=9 units yields…

A: topic - rate of change of function

Q: 5. √√64 .05

A:

Q: Q2/Test whether the differential equations are exact and solve those that are. (Answer only two) -y²…

A: We have to solve given differential equation.

Q: Find the Cartesian coordinates of the following points (given in polar coordinates). a. (1,0) b.…

A: topic - coordinate conversion x=rcosθy=rsinθ

Q: Can you elaborate you answer in b>? I cdont understand whiy it became 4

A: We have to elaborate why the angle is 4π3.

Q: For numbers 4-5, consider a plane bounded by the curve x = -y² + y +2 and the y-axis. The…

A:

Q: {CLO-2} Evaluate lim f(x) where (4x-1 if x3 O does not exist O 11 O 12 O 13

A: