Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in terms of x and y.) x² + 4y² = z², P(5, 6, 13) 10x+12y +z = 135 X

Q: 7. Determine all value(s) of the constant k so that the planes x+2y+3z = 4 and 3x + (k²+2)y+(7-k) z…

A: We need to find values of k.

Q: A business buys a computer system for $12000. The value of the system is depreciating and decreases…

A: We need to find out the value at the end of 3 years.

Q: 1. Given the algebraic function x² - xy + y² = 3 a. Find dy/dx v= O Option 4 y Option 2 y - 2x 2y +…

A:

Q: ind (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: solution is given below..

Q: Determining the Maximum and Minimum Values of Quadratic Functions A rocket is launched in the air.…

A: This question can be solved using the concept of maxima and minima

Q: #1 Cπ/2 ST 0 (8 + 4 cos x) dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: b) f(x)= x² tan(√4x+7)

A: Here we have to find derivative

Q: Evaluate the expression when x=-6. x² + 7x+8

A:

Q: Ldb + BOL + LB (BAL +dB) = 0

A: Given, αdβ+βdα+αββdα+dβ=0

Q: Use the Law of Cosines to determine the indicated side x. (Assume a-b-40. Round your answer to one…

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

Q: 3x2 + Sv 을 가

A: Given Expression:- 3x-12+4x12+x32

Q: 2 1. (2xy-3x²) dx + (x ² + 2y) dy = 0

A: 2xy-3x2dx+x2+2ydy=0

Q: 3. Find the derivative of each function by using the limit definition of the derivative! a) f (x) =…

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: given that,y=x5(1+2x)7 we know that, derivative formulas: (uv)'=uv'+vu' ddx(xn)=nxn-1

Q: Integrate. √ ( 7x² + 2/17 - 0²³) 0 3x 4+ dx = 0 +C

A:

Q: u 2.) du + (-1/2 − u²)dt = 0 t

A:

Q: Find the decomposition a = a + a₁ with respect to b if a = (3,4,2), b = (3, 4, 6). ab = (a||x, a|ly,…

A:

Q: Below are the graphs of 6 functions A-F. There are also graphs of 5 derivative functions 1-5. Match…

A:

Q: Find the derivative of the function. f(v) = (v−3 + 3v−2)3

A: to find out the derivative of the given function.

Q: 2x Eliminate the arbitrary constants of y=x²+c₁e²x+c₂e 2 3x

A:

Q: To create an object to display at the Art Museum of Philadelphia, Hao creates a solid of revolution…

A: If y is given as a function of x, then the volume of solid obtained by rotating the portion of the…

Q: Find the length of the following curve. If you have a grapher, you may want to graph the curve to…

A:

Q: 1 c) [xln (25) dx =

A:

Q: 1. Let f(x, y) = 4√√xy² + 4y +exy. a) Use local linear approximation to estimate 4√(0.1)(0.9)² +…

A: If f(x,y)  is a two variable real -valued function whose partial derivatives fx(x,y) and fy(x,y)…

Q: A radioactive material decays at a rate proportional to its amount. if the material has a half-life…

A: Given:If the material hs a half-life of 30 minutes To find what percent of the original msss is…

Q: Calculate the 3 × 3 determinant. (Use symbolic notation and fractions where needed.) -2 6 -5 2 7 2 2…

A:

Q: Consider the following complex numbers (b) (cle. Complete the following table Complex number 21 22…

A:

Q: The daily cost (in dollars) of producing LG ultra high definition televisions is given by C(x) = 3x³…

A: NOTE: Refresh your page if you can't see any equations. . the given cost function is  where…

Q: Calculus Find the volume of the solid generated by revolving the region bounded bythe graphs of y=x,…

A:

Q: Write the first trigonometric function in terms of the second for ? in the given quadrant. sec(?),…

A: Topic : Trigonometry

Q: Do the points (4, 3, −4), (4, 1, −1), and (4, 9, −13) lie on the same line?

A:

Q: Compute the partial derivatives: ?х 8z dy || 8x

A: Given that , z=8xx2+y2 find the partial derivatives.

Q: Consider the integral fa¹ In(a) Applying the integration by parts technique, let U = In(x) dv = x4…

A: This question is based on Integration by parts technique.

Q: The graph below is the function f(x) 3 2 OF -5-4-3-2-1 Find lim 24-1 Find lim 24-1¹ Olim f(x) 2411…

A: As x tends to Right side f(x) tends to -1 , therefore limx→-1-f(x)=-1

Q: 12 лухари у-х2-2х-я сил не 2x-9 and the tangent to the wave curve at the point whose X- coordinate…

A:

Q: дz дz Let z = sinh(7x + 8y). Find and ax ду дz ax дz ду || 7 cos(7x + 8y) 8 cos(7x + 8y) х х

A:

Q: Calculate the cross product assuming u xw = (8,6, -2) (Use symbolic notation or fractions where…

A:

Q: A company manufactures two types of athletic shoes, jogging shoes and cross trainers. The total…

A:

Q: S Radoptimal 5 find the limit and deternue of the functio is continous at the poult buy et…

A:

Q: Solve the following for C. (Assume that C > 0) C (4x+8) dx 0 C = = 90

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

Q: Find the Laplace transform of the following: (b)sin 2t + Ans: (b) 2 3 cos 3t 2 2 13+4+3² +9 2

A: I am attaching image so that you understand each and every step.

Q: Let u = and v = Select all of the vectors that are linear combinations of {u, v}. (Check every…

A:

Q: culate the cross product assuming that u x v = (6, 7, 0) vx (u + v) = (a, b, c) e symbolic notation…

A: Given query is to find the cross product.

Q: Find the average rate of change of the function over the given interval. R(0) = √30 + 1; [1,5]

A:

Q: The tangent line to y = f(x) at (4, -3) passes through the point (1,1). Compute the following. a.)…

A: This question can be solved using the concept of two point form of line and derivatives

Q: Find the equation of the tangent line to the graph of f (x) = 6x2 - 4x + 1, at x=1.

A:

Q: 11. f(x) = a sinx - b cos x + c

A: f(x) = asinx -bcosx +c  Given We have to differentiate it . Steps are given below

Q: Select the following equations that are true. 01² +2² +3² +4² +...+100² = 5050² 1 1 0 1 1 + 101 1 0…

A: Given 1.  12+22+32+42+⋯+1002=50502 2.  111011101+123456-4-5-6=234467-3-5-5 3.…

Q: 3 If f(x) = 2x√x + ²√ find f'(x).

A:

Q: П Find the length of the curve y = In (2 sec x) from 0≤x≤6 Set up the integral that gives the length…

A: