The equation yz = 2ln(x + z) defines a surface S in R. The point P(0,0,1) is on the surface. (a) Write down the equation of the tangent plane to S at P. (b) The equation for S defines z implicitly as a function f of x and y. So f(0,0) = 1. The tangent plane to S at P is also the graph of the linearization of f(x,y) at (0,0). Use this linearization to find an approximate value for f(). When x = and y = , then z is approximately equal to

Q: 1)2xsin-13x

A: Given     write

Q: 2. Calculate the following limits. Justify your answer. L'Hopital's rule Rule ) (without using 2x +1…

A:

Q: If 5a + 3x + ry = 1 and y(1) = - 7, find y'(1) by implicit differentiation.

A:

Q: The population P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by P =…

A:

Q: 5. A squirrel runs along the edge of a fence. The graph of the squirrelľ's velocity v(t), in m/sec,…

A:

Q: AB is the vector from the point (1, –2) to the point (5, 1). Find a unit vector in the opposite…

A:

Q: Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.) f(x) = 2…

A: Given, f(x)= 2cos(2x) For, x=0=> y= 2cos(0)= 2  => y-intercept= (0,2) For, y=0=> 2cos(2x)=0…

Q: Sind the a rea betwee h 2. メニリ and メ=9で

A:

Q: Select a scatter plot of the given data. 4% 6% 8% 10% 12% 14% t 28.01 18.85 14.27 11.53 9.69 8.38 90…

A: topic - exponential decay function

Q: The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the triangle of…

A: Here we have the perimeter of the isosceles triangle = 38 m,  Let the equal sides of triangle = x…

Q: 3x - - 4y 2xy 96

A:

Q: A company manufactures and sells DVD's. Here are the equations they use in connection with their…

A: Here we will find the functions,

Q: In 2 10e a 4.

A:

Q: Question 3 > Use part I of the Fundamental Theorem of Calculus to find the derivative of 14 dt f'(x)…

A:

Q: Q2\Find the point at which the tangent to the curve y = v4x2 +1-2 has its slop 2

A: Tangent to curve

Q: Question 1 If z=lm/x*+ y² + un /x²+y²+-tan 12 then the numerical value of dy? dx2 is equal to...-

A:

Q: Complete the table for a savings account in which interest is compounded continuously. Amount after…

A: Given query is to find the time taken to double the investment and amount after 10 years.

Q: Find the domain of r(t) and the value of r(t,). NOTE: Round your answer to two decimal places when…

A: Domain

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: Suppose log ,2 = a and log ,3= c. Use the properties of logarithms to find the following. log b…

A: Now,                logb1728b=logb1728+logbb=3logb12+logbbUse logbb=1.=3logb12+1

Q: Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.…

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

Q: seco SI sin 20 dp dộ dên o Jo

A:

Q: We must also convert dx into an expression involving u. We know that du dx, and so x3 dx = X du.

A:

Q: Fundamental Theorem: 2x sin t -dt. Find the value of f'(x). t2 +1 Let f(x) = | %3D

A: We can solve this as follows:

Q: Evaluate (if possible) the sin

A: answer is in next step

Q: G(x) = tant dt Find G(1) = Find G' () =

A:

Q: The graph below is the function f(x) 5+ 4 3 -5 -4 -3 -2 -2 -4 -5+ Find the following. If no value…

A: Given problem :-

Q: Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon…

A: Given; A=Ao e^(-0.0001213)

Q: Let y tan(3x + 6). Find the differential dy vwhen a 2 and da 0.4 Find the differential dy when z 2…

A:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A:

Q: For problems 1 & 2 determine the length of the vector function on the give 1. ř (t) = (3 – 4t) i +…

A: First differentiate the given vector function and the find its norm and then find its length by…

Q: Evaluate the line integral F. dr, where F (x, y) = (3+2xy) i+ (x² – 3y²) j and C is the curve given…

A: Given problem:-

Q: Sketch the region from the first quadrant, bounded by y = 2x2, x = 0, and x- 2y + 3 = 0, and find…

A:

Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: Let g(x) be a differentiable function for which g'(x) > 0 and g"(x)< 0 for all values of x. It is…

A: Given query is to find the possible value for g(7).

Q: Find r(t) if r'(t) = ti+ e'j+ 3te3t k and r(0) = i +j+ k. r(t) = Need Help? Read It

A:

Q: d 6. dx sin(t) dt

A:

Q: /121 - s" 12t – 5t' +9 dt = +C. (b) u14 + 4.5 Jū du =| +C (c) 1 dx = 5x6 +C.

A:

Q: (a) Explain why the function f(x) = e² is not injective (one-to-one) on its natural domain. (b) Find…

A: We are allow to solve only three subpart.  If you want rest of part please upload separately

Q: 30° D.

A: Please see the below picture for detailed solution.

Q: Use the properties of logarithms to verify the equation. -In(24) - -(3 In(2) + In(3) -In(22. -In(24)…

A:

Q: Use long division to divide. (5x - 12x? - - 4x + 3) ÷ (5x + 3)

A:

Q: Find the particular solution determined by the initial condition. ds 17t +7t-6, s(0)= 86 dt %3D The…

A: The given differential equation is ; ds/dt = 17t2+7t-6, s(0)=86

Q: Q1\ Differentiate the following x+1 2)y = ln- x-2

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

Q: he area is sketched below. ide the area below the curve into ple point of each rectangle. Ske AY

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +4 1' lim t00 9t2 + 10' 8t. |(?,?)

A:

Q: If f(x) = (3,-1) what are the coordinates of f(x) : +1?

A: To find the coordinates of the new formed function.

Q: Find the exact values of the six trigonometric functions of the angle 8 shown in the figure. (Use…

A:

Q: a) Determine the position function, s(t), of an object if the acceleration function of the object is…

A:

Q: Identify the value of the function f(x)=log10x at x = 315, Round to 3 decimal places. 3.498 2.498…

A: