5.) Find the limit. When necessary, state that the limit does not exist. x² + 3x-18 lim Xx-3 x-9

Q: Find the Average Rate of Change of the following function over the interval [2, 5] (That is, from t…

A:

Q: r₁(t) = (14,3, 11) + t (−4, −1, −3) r₂(t) = (0.5, 4, −11) + t (1, 2, −4) Find the point of…

A: Given: Equations of lines:r1(t)=14,3,11+t-4,-1,-3r2(t)=0.5,4,-11+t1,2,-4

Q: (4) Find the volume of the solid obtained by rotating the region bounded by y y=√x about the y = 1.…

A:

Q: At what points is the following function continuous? 3 x - 125 x²2²-25 f(x) = 7.5, 4, X#5, x# -5 x =…

A: Given function:- fx=x3-125x2-25x≠5,x≠-57.5x=54x=-5 Condition for continuity at x=a…

Q: Express the following functions in the form u+iv • f(z) = \n (1+z) P

A: Given function is: f(z)=ln(1+z) Let z=x+iy

Q: 2. Is it possible for a function f(x, y) to satisfy both f(1, 2) = 5 and f(0,0) = 5? If yes, gi- an…

A:

Q: Recall the integration by parts formuala: Complete the following computation = [f(a)g'(x)dx =…

A:

Q: What is correct form of the particular solution associated with the differential equationy"=8?

A:

Q: 2Y+ 3/4X=Z/3

A: The given expression 2Y+34X=Z3 we have to solve the expression for X,Y and Z

Q: The Z-transform of the following function f[k] = 2.2k + (-5)* - 33 (-4)* is so the constants A and B…

A:

Q: 2. CALCULATE THE VOLUME OF A RIGHT CIRCULAR CONICAL CONTAINER (IN LITERS) WHOSE HEIGHT IS 4 YARDS…

A:

Q: A sphere is tangent to the x-y plane, the x-z plane and the y-z plane and it's center is the first…

A:

Q: dt z = cos(x + 4y), x = 5 t ³, y = 8/t

A: We need to find out the value of dzdt

Q: Find the integral involving secant and tangent. (Use C for the constant of integration.) Itan tan²…

A:

Q: If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c…

A:

Q: maximum

A: The fine F for violating these limits is $10 for every mile above the maximum or below the minimum.…

Q: 18. Use Cylindrical shells method to find the volume of the solid that results when the area of the…

A:

Q: 1) Find the difference quotient of f(x)=x². That is, find f(x+h)-f(x) for h#0. Simplify so h that h…

A:

Q: 6a + 24 3a-24 2 으 - a -16 a ²-2a-48

A:

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: Solve the given equation on the interval 0 ≤ 0 ≤ 27: tan 0+1=0

A:

Q: 4. Evaluate: lim(x² - 10x) x→6

A: This question can be solved by replacing x by 6 in the expression x2-10x.

Q: Q: A. Find if w = xy + z.x= cost.y = sint and z = t at t = 0.

A:

Q: Consider the method of Variation of Parameters for solving the general linear equation of first…

A:

Q: The

A:

Q: limx→0 sin 2x 2x²+x

A:

Q: 6 5 4+- 3 2 1 1 +- I lim 1-8 lim lim → 4¹ 1 0 1 2 y = f(x) →4 T T I T 1 Enter each answer as a whole…

A:

Q: 3. lim_ f(x) = X-3- lim f(x) = X-3+ lim f(x) = x-3 f(3) =

A:

Q: Procedures and Problem Solving Library of Parent Functions In Exercises 5-8, use the graph of the…

A:

Q: using

A:

Q: 1. Find the derivative using the Fundamental Theorem of Calculus, Part I, without evaluating the…

A:

Q: Parameterize the line through P = (-4,-4) and Q = (0, 3) so that the points P and Q correspond to…

A:

Q: 3) Prove that : tanz = 올n(부를) In

A:

Q: observing the outside temperature rise. What is the relevant independent variable here? The…

A:

Q: question 21. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

A: We will find the required.

Q: Given the graph of f(x) = √√x as shown, graph the function 5ƒ(x) – 5. -7 -6 -5 -4 -3 -2 -1 7- 6 5+…

A:

Q: complete

A:

Q: Find the following limit. Answer as a fraction or integer (no decimals.) x² x +9x-22 x²-4 lim X-2 -

A:

Q: Use the given conditions to write an equation in point slope form and slope intercept form. 8. Slope…

A:

Q: Find a parameterization for the curve shown in the figure below. r(t) = where = -1 1,0 -1 <t<

A:

Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: 5. I Find the area of the region enclosed by the curves y = 3x³ - x²-10x and y=2x-x². (x ≥ 0) (a)…

A:

Q: y' xe2y subject to initial condition of y(0) = -1 =

A: Please see the below picture for detailed solution.

Q: Use the Chain Rule to find dz/dt. z = xy9 − x2y,    x = t2 + 1,    y = t2 − 1

A:

Q: R is the region bounded above by the function f(x) = −4+7 and below by the function g(x) = - + 2…

A: We need to draw graph.

Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ &amp; v→ Nonzero scalar α v→=αu→

Q: write true or false for each statement  1. {∅}⊆{∅,{∅}}   2. ∅⊈∅   3. {∅}∈{∅}

A: The answers are given below:

Q: Find the differential equation by eliminating the arbitrary constant/s. y = = Aex cos x + Bex sin.x…

A: We differentiate the number times as the number of arbitrary constants present in the equation and…

Q: Calculate the cross product assuming that = (-2, -8, -2) u x w = (4u − w) × w = (100)

A:

Q: 1. Determine the derivatives of the following functions (a) y = (x² - 2)²

A: We can determine the derivative in the below steps.