Let f: R2 → R. At some point, a , we have that f(a) = 5 and that Vf(a) : What is the equation of the plane tangent to f at the point a ? Enter your answer as a function of z and y:

Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

A:

Q: In cos x (1) lim x→0 tan x2

A: Let's find.

Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: Find the sum of the first 100 terms in the arithmetic series 1+2+ 3+4 + ... + 100.

A: To find the sum of first 100 terms of given arithmetic  series.

Q: II. Find the Inverse Laplace of the following 2s-9 d. s² +2 1 е. (s²+1)(s²+4s+8)

A: As we know the Laplace transform identity; 1). L-11s2+a2=1asinat 2). L-1ss2+a2=cosat 3).…

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: Question 2 Find the differential dy: y= sin O dy E In a + sin( rVE dr Cos ( xY O (E) None of these…

A:

Q: C hnd the firet order parho derivohve of 32 4 5 1. 2) %3D *y-16y²23+43x %3D h Cs, t) =° E*In ts3) +…

A: Solution is here

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: We have to find dR/dt .

Q: 2x-9x+2= 4x-13

A: Given query is to find the value of x.

Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

A:

Q: b) Find the values of a and b so that the unction f(x) = x + ax + b has a local maximum at the point…

A: Given function f(x)=x2+ax+b The local maximum at the point(7, -6) We need to find a and b

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: Given query is to find series converges or diverges.

Q: 3. If a = 2 i-3 j+5k and b = -3 i+6k, determine a simplified vector for each of the following in the…

A:

Q: z-1 Suppose the symmetric equations of lines l4 and l, are = 2 – y = z and x = -1, = 2 respectively.…

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

Q: 4 Y= 5/(sin3x +cos3x)

A:

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

A:

Q: 15 x2-35 + 25 A B Let f(x) The partial fraction decomposition of f(x) where A, B, C EZ. (x - 1)(x…

A:

Q: Зх—5 dx (х+1) (х+2)2

A:

Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

A:

Q: Find the absolute maximum and absolute minimum of the function f(x)=2x^5/2 /5−2x^3/2 /3−1 over the…

A:

Q: -2 is a critical number of the function f(x) = /2x - x2, Select one: O True O False

A: The given function is  f(x)=sqrt(2x-x2)

Q: Find and sketch the domain for the function. sin (xy) f(x,y) X* + x² + y? - 81 ... Find the domain…

A: Given

Q: 2x J(x – 3)2 A = 6, B = 2 A = 2, B = 6 A = 2, B = - 6 A = - 2, B = - 6 A = - 2,B = 6 None of the…

A:

Q: explain

A: We will check if the fundamental theorem of Calculus is applicable.

Q: The interval of convergence of the series 41+2n (x+3)" is - -- 5n+1 16 16 Select one: O True O False

A:

Q: Q5: S x dx ajconverges to 1 bjconverges to cconverges to- 4. d)diverges 25-2

A:

Q: Activity 3: 1. ſx²dx 2. SVx?dx 3. S(x³+x²)dx 4. SVx*dx 5. fx-2dx 6. S tan?x dx 7. S(1 – cos u)du 8.…

A:

Q: Find all the second order partial derivatives of the given function. ​f(x,y)=xy2 + yex^2+5

A:

Q: x-1 8. y = log х+1

A:

Q: Determine the Laplace transform of 2et cos (6t - T). CO 8-4 3/3 (금) s2-8s+52 s2-8s+52 ㅇ (-) -85+52…

A:

Q: ladder away

A:

Q: The power series representation of 1 f (x) = 5x +4 is: O 5 25 125 x+... 256 4 16 64 25 125 x++...…

A:

Q: Given the differential equation dy dx (x – 1)(x + 2)' x +1 y = 1- y > 1, x> -1. a) Find the solution…

A: Here we have given a linearly differential equation :

Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all æ in [ – 8, 4], and| f(x)dx = 76 and L…

A: Concept: Mean value theorem: The mean value theorem states that if a function f is continuous over…

Q: Find the derivative of the function at Po in the direction of A. f(x,y.z) = xy+yz+ zx, Po(-1,1,2).…

A: Given :f(x,y,z)=xy+yz+zx

Q: Change the Cartesian integral into an equivalent polar integral. 3 0-x SS (P+y?) dy dx = J JO dr de…

A:

Q: Practice Problems. Find all of the first order partial derivatives for the following functions. (a)…

A:

Q: Determine the exact value of 2 sincos cos 12 12

A: Given query is to find the exact value of the expression.

Q: 7x – 2r – 12 For the function f(x) =- x² +6 a) Find the equation of the non-vertical asymptote b)…

A:

Q: 9–x² x2

A:

Q: 3. Out of frustration, Maxine throws a stone into a river. This caused ripples in the form of…

A:

Q: Consider the vectors a = 4 i+ 8 j-8k, b = 2 i +k and c = 4 j-5k. Are the vectors a and b+c…

A:

Q: What are intervals of concavity of the function f(x) = -2x – 6x² – 3 ? a. Concave upward on (-o, 1)…

A: Concept: Concavity: If the line connecting two points is above the graph, or if the first derivative…

Q: Find the area of the triangle having vertices at (−2,3,1),(1,2,3) and (3,−1,2)

A:

Q: 2л + 3 dx 4г2 — 4х + 5

A:

Q: Find the interval of convergence of the series E1 00 n=1 n8" O (-1, 1) O (-8, 8] O (-8, 8) O (-8, 8)…

A: We have to find out series

Q: lim X- Sin X X3

A: