Find positive constants a and n, such that n - 4 > an for all n > n,.

Q: Cadmium, a heavy metal, is toxic to animals. (The chemical abbreviation fo rooms, however, are able…

A: Given data: X 0.24 0.59 0.62 0.16 0.77 1.33 0.92 0.19 0.33 0.25 0.59 0.32…

Q: Consider the following series. 2 n² + 4n +3 (a) Determine whether the series is convergent or…

A:

Q: Find the radius of convergence and interval of convergence of the series. 00 (8n)! n=0 R = I =? v ?…

A: Given series is

Q: Find an integer a such that a 400 = 1(mod 3911).

A:

Q: x² – 10x – 5 dx |x- 1)-(x² + 1)

A:

Q: the following situation, find the mean and standard deviation of the population. List all samples…

A: See the Excel output

Q: if f(1) = 10 and f'(x) = 2 for 1≤ x ≤4, how small can f (4) possibly be?

A:

Q: 4. Consider the vector field F(r, y, z) = (x, y, z). (a) Sketch a picture of F. (b) Calculate div F.…

A:

Q: For each equation of a surface given in cylindrical coordinates, sketch the surface and describe it…

A: Given: a) r = 7 b) θ =π2 c) z = 2

Q: Consider the following function. f (x) = ln(1 + 2r),a=3,n= 3, 2.6 < 1< 3.4 (a) Approximate f by a…

A: (a) Let’s make a value of some derivatives of f.

Q: 3. In this problem we will find the mass of the tetrahedron in the first octant bounded by the…

A: Given the tetrahedron is boubed by the coordinate planes x=0,y=0,z=0,and the plane x+2y+3z=6, the…

Q: Express the number as a ratio of integers. 5.21345

A:

Q: 2. Sketch two complete cycles of the sinusoidal function described in the scenario. The temperature…

A: Given: The temperature of a liquid varies sinusoidally as it heated and then cooled repeatedly. The…

Q: 100 nd a number between 0 and 12 that is congruent to 2"modulo 13. Show your work.

A:

Q: 5. Let S be the part of the paraboloid z = 9 – a² – y² (with upward orientation) that lies above the…

A:

Q: Refer to image

A: Solution

Q: Find and classify the critical points of f(x, y) = (y – 2)x² – y². Justify your answers.

A: We use second order partial derivative test to find out maximum, minimum and saddle point

Q: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even.

A: Given: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even

Q: 5. Find the arc length of one loop (petal) of the polar rose r = 6 sin(40) . How did you decide on…

A: We need to find the arc length of any one of the 8 petals from θ1 to θ2 L=∫θ1θ2r2+drdθ2dθ Where…

Q: Prove that gcd(a + b, a - b) = gcd(2a, a – b) = gcd(a + b, 2b). Show your work! Justify each step.

A:

Q: Let A and B be sets. The union of A and B is A U B = {x|x E A V x € B}. The intersection of A and 3…

A:

Q: 2x + 3y Find -dA, where R is the parallelogram enclosed by the lines 4x – 4y -- 2x + 3y = 0, 2x + 3y…

A:

Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

A:

Q: Consider the function f(x,y) = y² + 2xy. a. Find the directional derivative of f at the point (2,…

A: using formula for directional derivative