Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

A:

Q: Find the normal vector to the level curve f(x, y) = c at P. f(x, y) = 6 - 4x - 7y c = 6, P(0, 0)

A:

Q: 3. Determine the radius and interval of convergence of 8 k=2 7k (x - 5) k k

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

A: Given that   f(x,y)= z = x2-2xy+y2     So,  this can be rearrange as…

Q: the first five terms of the geometric sequence. a n = 4a n-1; a 1 = -4

A:

Q: Use synthetic division and the Remainder Theorem to find the indicated function value.…

A:

Q: 2. For Luce Landscaping, the total revenue and the total cost for yard maintenance of a homes are…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…

Q: Compute the determinant of the matrix by cofactor expansion. 325 114 O-56 -8 O110 8

A:

Q: If the first 5 terms of a geometric sequence are {12, 6, 3, the formula for the nth term in the…

A:

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

A:

Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

A:

Q: f(x) = x²-3x + 7 concave upward concave downward X X

A:

Q: Use the implicit differentiation to find dy/dx. Then find the slope of the curve at the given point.…

A: By using the implicit differentiation to find dydx. Then to find the slope of the curve at the given…

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: W need to estimate slope.

Q: increasing decreasing f(x) = sin(x) + 1 T 2 + πn,∞0 0 < x < 2π (-∞0, 1/2 + 1) X X

A:

Q: yey dx = (y² + 2x e¹) dy

A: The given differential equation,     yeydx=y3+2xeydy

Q: Use Linear Approximation to estimate Af = f (7.01) - f(7) for f(x) = x². (Use decimal notation. Give…

A:

Q: 4. Use the bisection method to approximate the root of f(x) = 2x² [0, 1]. Let € = 0.1 be the margin…

A:

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

A:

Q: Use the given information to find the exact value of the trigonometric function.  cos θ = 1/4 , csc…

A:

Q: Sy²sin (2y) dy

A: Integration by parts.

Q: 1 Σ 3 k=4 √k -5k + 20 By the properties of the p-series, Limit Comparison Test, this series…

A: To find whether the series is convergent

Q: Find the length and width of a rectangle that has an area of A square centimeters and a minimum…

A: We can find the correct answer by checking the individual options as below.

Q: In reference to the following function,  f (θ) = (θ − 3) cos(θ) Explain why the graph of f lies…

A:

Q: Let f(x)=√x - 7. Then lim h→0 f(3+h)-f(3) h 1 2√3 If the limit does not exist enter DNE.

A: Laplace transform:- If limh→0f(h)g(h) is of the form 00 then limh→0f(h)g(h)=limh→0f'(h)g'(h) and so…

Q: Part b: We consider the function f(x, y) = x sin y - y cos x + y Find fx(x, y), fxy(x, y), and fxyx…

A:

Q: Which of the rectangles below are right rectangles? 25-4 20 15 10 63 BODEX 0 5 10 15 20 25 Select…

A: This question can be solved using the concept of estimating the area under curve using left and…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: This question can be solved using the concept of the stated theorem 13.9

Q: Find the solution of the following IVP: y(t) = = dy dt 2ty=9t²e, y(0) = 5.

A: We have to solve the given IVP.

Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an 8 Σ (-2)^…

A: Understanding of the ratio test is required in order to understand this problem.

Q: -1 0 -t³+1 2 3+² e dt

A:

Q: O ди If u = f(x,y), x = g(w) and y = h(w), using Chain Rule, what is aw O ди aw ди Əw || O all of…

A: u=fx,y, x=gw and y=hw

Q: e² 1+2e +e S Select one: O A. dx 1+6² 2 1+6² +C +C O B. OC. +C OD. +C -2 Ite -1 1+e

A:

Q: Which of the following rational functions is equivalent to the partial fraction decomposition Select…

A:

Q: Use Newton's method to approximate a root of the equation 3x7 + 7x² + 2 = 0 as follows. Let 1 = 1 be…

A: Follow the procedure given below.

Q: Question 35 If z = x arctan 0 - 4 OFF O undefined ◄ Previous (²).find əz əx at x = 0, y = 1, z = 1.

A: To find the partial derivative of z with respect to x.

Q: Integrate farcsin 3x da Select one: O A. xarcsin 3x + √1-9x² + C O B. xarcsin 3x + √1-92² +C O C.…

A:

Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

A:

Q: integral of cos x sin^3 2 x dx

A:

Q: Evaluate. e14x (e14z +13)² (Note that the constant of integration is already included) dx +C

A:

Q: or the function f(x)=sin(x), write Newton's formula as xn+1=F(xn)=xn−[f(xn)f'(xn)] for solving…

A: The given function is f(x)=sin(x) We need to solve for, f(x)=0 using Newton's formula:…

Q: Find a normal vector to the level curve f(x, y) = c at P. X = x² + y² P(5, 5) f(x, y) = C = 100

A: To find the normal vector.

Q: Solve the triangle. 13 B A 8 6

A: We have to solve  all parts of triangle.

Q: Carbon-14 decays at a regular exponential rate. The half-life of carbon-14 is approximately 5730…

A:

Q: Consider the function f (x) = x³ -12x^2 + 36x = x (x-6)^2 to answer the following questions.   1.…

A:

Q: Find aw/as and ow/ot using the appropriate Chain Rule. Function Values w = y³ - 7x²y x = e³, y = et…

A:

Q: Consider the infinite series > Evaluate the first four terms of the sequence of partial sums. k=1…

A: Given that infinite series       ∑k=1∞1k+3       We have to evaluate first four terms of the…

Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

A:

Q: Find the general solution of the differential equation. y(4) + 2y″ + y = 7 + cos(2t). NOTE: Use C₁,…

A: To find the general solution of the given differential equation.