Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point P(1,0,0). Using a coefficient of 1 for z, the equation of the plane is = 0.

Q: √x³√1-x² x2

A:

Q: 6. Find the intersection of the line I and the plane . 1:7=(4,-1,4) +t(5,-2,3) 2x+5y+z+2=0

A:

Q: . Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Topic:- function  and application of integration

Q: You are to form 3-digit numbers from the digits 1 to 5. How many 3 digit numbers can be formed if a)…

A: Solution of given question is written in below steps.

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: 12. What is the amplitude of the graph below? y 4 0 8+ 7+ 6+ 5+ 4+ 3++ -1- -3+ -4+ -5- -6+ -7+ -8+…

A:

Q: f(x) = x³ +7x² - 5x

A:

Q: 9. f(x) = xe−2*, a = 0

A: According to bartleby guidelines I can only answer the first question of the two given.

Q: x²y" - 3xy' - 2y = 0

A:

Q: (2x²² +ex) dx + (x² + 1) = "² dy (x²-y) dx x dy

A:

Q: 6. If fand g are two differentiable functions at x, then 7. The derivative of the identity function…

A:

Q: dw dw For the functions w= - 4x² - 2y2, x= cost, and y= sint, express as a function of t, both by…

A:

Q: NIFN dx √2x (√2x + 9)

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

Q: HOW DID YOU GET THE ANSWER??

A: Let's find general equation of circle.

Q: 3) Using the trafe boich unte, find the following integrats 2 Ⓒ S x lnx d x Aslo 1

A:

Q: Find the derivative of the function at Po in the direction of u. 2x-y g(x,y) = 5xy +6 Po(1,-1),…

A: We need to find derivative of the function.

Q: Consider the initial-value problem y' = 8x³y, y (2) = 5 Solve the initial-value problem to find the…

A:

Q: 14 Find f(x) dx for each graph of y = f(x). 0 (a) Q (b) 16- 0 888 16 16+ y BABBARBADE 0 16 Q

A:

Q: Convert each pair of polar coordinates to rectangular coordinates 1. (1, 60 degrees) 2. (1, 300…

A:

Q: x==2t X 1 1-y = Given: line ₁ = -8 and ₂ = = y = 2+2t. 3 2 z = 6 + 2t 1. If the given lines…

A:

Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (2,4)…

A:

Q: əz Let z = x² + y³, x = 2st and y = s-t². Compute for and ar

A:

Q: a. lim+ 2x 3x²

A:

Q: 11. Find the limit using algebraic techniques. The limit of f(x) = -4 O- 0 O=¹ x+4 2x²+5x-12 as x…

A:

Q: In 1000 5 X limx→ +00 X

A:

Q: 4. Solve each for angles between 0° and 360°. (Round final a steps.) a) cos=-0.2186 b) 5-2 sin0 =…

A: The solution as follows :

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

A:

Q: Find a power series representation for the function and determine the interval of convergence. (Give…

A:

Q: Find the center of mass of a thin plate of constant density & covering the given region. The region…

A: Let's find center of mass.

Q: 2 2 dx 2x (V2x + 9)

A:

Q: Without using the graph, determine all critical points of e2x − 2x and classify them as local max,…

A:

Q: Find the inverse of the function on the given domain. f(x) = (x−5)^2, [5,∞)

A:

Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

A:

Q: Given : f(x) = 10 -x 9(x) = x² - 4x-2 Find and simplify (fºg)

A:

Q: 4. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate…

A:

Q: Evaluate f Select one: cosha -da cosh²a-1 a. -sinhr+C O b. -cscha+C C. O d. -coshr + C none of the…

A:

Q: Evaluate the integral da Select one: a. +C O b. о с. O d. - Inz - -/+C 2x inz -/+C - 2in1+²+C N 4

A:

Q: S²₁ A Select one: dw w√w²+3 a. 0.0128 O b. -0.0234 0 с. c. -0.0128 O d. 0.0234

A:

Q: xy a. Compute the first- and second-order partial derivatives of f(x, y) = xe with respect to both x…

A:

Q: 2.1 Limits 2 1. Use the graph to estimate the limits or explain why the limits do not exist. y (a)…

A:

Q: Find the derivative of cos-¹(sin x)

A:

Q: If repetition is not allowed, in how many ways can we arrange ♣, ♠, ♦, and ♥ a) four at a time? b)…

A:

Q: Find the gradient of the function g(x,y) = xy² at the point (3, -1). Then sketch the gradient…

A: Given:        Function gx,y=xy2   The gradient of function                  ∇gx,y=gx,gy   Taking…

Q: (a) From Standard Form to Slope-intercept Form and Vice Versa (b) From Standard to Intercept Form…

A:

Q: Find y (2) if D.E. 2 dx +3y=sin 2x₁ y(0) = 6

A:

Q: RIN Find the linearization L(x,y) of the function f(x,y)=e4x cos (3y) at the points (0,0) and 0₁-…

A:

Q: 7 =-=—=x² Find the center of mass of a thin plate of constant density & covering the region bounded…

A:

Q: 10. Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Given ,  We have to find the equation of the curve whose slope is the inverse of the sum of the…