Evaluate the limit, or type "DNE" if the limit Does Not Exist: x² - xy lim (x,y) → (9,9) √x √4

Q: 5) Find the divergence of (√x² + y² + z 5) ki vj + zk)

A:

Q: Match the following functions with the general shape of their graphs. Functions f(x) = ln (x + 2) -…

A:

Q: Evaluate the line integral, where C is the given curve. 2 xeyz ds, C is the line segment from (0, 0,…

A:

Q: Find the Taylor series (general form) of f(x): 1 X centered at x = 1.

A:

Q: 2 Find the area between the graph of y = 5 – 5x³ and x-axis and − 1 ≤ x ≤ 8 using properties of…

A:

Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

A:

Q: The marginal cost function C'(x) was defined to be the derivative of the cost function. If the…

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

Q: Find the limit (if it exists). lim f(x), where f(x)= x+1- [x³ +2₁ x < 1 x+2, x ≥ 1

A:

Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: 1) Let an = 3+2(n-1). Write the first 5 terms of an. Find Σ10% ακ k=1

A:

Q: 20) Explain the idea behind l'hospitals vule.

A: use an  example to understand the l hospital rule.

Q: = Find the area of the region that is completely bounded by the two curves f(x) = g(x) = x² − 7x +…

A: Given query is to find the area of the region.

Q: If y is inversely proportional to x, and y = 9 when x = 6, write a formula for y in terms of x. Use…

A: Given y is inversly proportional to x let k = proportionality constant

Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A:

Q: Inverse Laplace transform of 2 s-5 2 + is s²+16 s³ f(t) = 2cos(4t)-5sin(4t)+t² F(s) = Select one: O…

A: We are required to find if the inverse Laplace transform of F(s) is True or False

Q: Find a Cartesian equation for the curve and identify it. cos(20) = 1 O limaçon Ohyperbola O circle O…

A:

Q: Find the derivative of the function. y' = y 1 - x² - x cos-¹(x)

A:

Q: Determine the values of constants a, b, c, and d so that f(x) = ax³ + bx² + Determine the values of…

A: Given,            fx=ax3+bx2+cx+d has a local maximum at the point 0,0 and a local minimum…

Q: A ladder 15 feet long is leaning against the wall of a house (see the figure below). The base of the…

A:

Q: Find the Equation for the Graph of a Logarithmic Function (-4,3) (2,4)

A:

Q: (a) Find the velocity v (t) - |a| (b) Find the acceleration function. 71 sin (a) e7 [7 sin(81) + 8…

A:

Q: Find the value of a that makes the following function differentiable for all values of x. g(x)= ax…

A: According to question, Given Function,gx = axif x&lt;0x2-7xif x≥0

Q: Find a polar equation for the curve represented by the given Cartesian equation. x² + y² = 4cx k

A:

Q: Find the sum of the series 65+ 513 5/9 + LO 5 27 - 5 81 +

A:

Q: (6417 #3 p. 357) Find the average value of f(x) = 6r-r² f(x= on the interval 2<z≤8

A: Given function is f(x)=6x-x2 and the interval is 2≤x≤8.

Q: (th) h B) none existent 2) lem Cos ho A) | TheR c) 0 D)(-1) E) None

A:

Q: Find dy dx by implicit differentiation. x²+2x+11xy-y²= 16

A: We have to find dy/dx.

Q: Use the graph of f(x) shown below to answer the questions J'(x) O (a) Find lim f(x). x-1 05 01/1/20…

A: see below the answer and explanation

Q: DETAILS The velocity of a skydiver, in feet per second, t seconds after jumping out of an airplane,…

A:

Q: Differentiate. y' = y = 3 sec(x) - csc(x)

A:

Q: 2. Find an equation for the tangent line to the cycloid x = et + 3, y = t² et - 3et + 2 at the point…

A:

Q: Consider the following function: f(x) = −x4 + 8x2 + 2   Enter the x-values of any local minima,…

A:

Q: Given that ƒ(x) = x² − 8x and g(x) = x + 5, find: a) (fog)( − 1)= b) (gof)( − 1)=

A: Given query is to find indicated composite function.

Q: An equation of an ellipse is given. ²+12²=1 (a) Find the vertices, foci, and eccentricity of the…

A:

Q: Identify the open intervals on which the graph below is increasing and decreasing. -5 -4 -3 -2 -1…

A: Solve the following

Q: If a principle of $4000 is invested at an interest rate of 6%, how many years will it be until the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 13…

A: We will find the required.

Q: Find the values of sin(0), cos(0), and tan(0) at the given points on the unit circles in the figure…

A:

Q: Find the equation of the line through the point (-5, 4) and perpendicular to the line y = 2-5.…

A: In this question, we want to find a equation of the line perpendicular to the given line passing…

Q: Is the function T(s) = (6s-4) (es-5) a power function? If so, identify k and p such that T(s) = ks².…

A: The given function is:T(s)=6s-4es-5

Q: Question 1 ( (a) ) ) For the function (b) ( transform 3 f(t) use the definition of the Laplace…

A: Given function is (a) f(t)=30≤t&lt;2e2tt≥2and (b) L-13(s+5)(s-2)

Q: For what values of h are the given vectors linearly dependent? 5 -20 -3 12 5 4 6 52 3 h Vectors are…

A:

Q: Consider the following parametric curve. Answer parts a and b. x = 4+2t, y=1-6t; t = 2 a. Determine…

A:

Q: The marginal cost of producing x units of a certain product is  75 + 1.4x − 0.006x2 + 0.00004x3…

A:

Q: The function w(z) represents a package's corresponding weight in grams when the package's weight is…

A: Given query is to find the meaning of the inverse function.

Q: Find the area of the given region. Use a graphing utility to verify your result. y = 1 + In x³ X y 1…

A: We can find the area of the region .

Q: Which of the following represents a geometric sequence with a common ratio r = 5?  1 2, 10, 15, 75,…

A:

Q: Q lan for the conic based Yon: Ellipse with major verti #) and a focus point at (9,4_ = sketch and…

A: SOLUTION: Given  that  an ellipse has major vertices at (-5,4),(11,4) And focus at (9,4) Now we have…

Q: Differentiate the function. F(t) = tº + e⁹ F'(t) =

A: Here is the solution:

Q: (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

A: