Find y'' for y = 4+ or y= (4 + ³) ³. X y"=0 3 5

Q: By expressing (") and (, "₁) i in terms of factorials, show that () + (₁²₁) = (^#¹).

A: nr+nr-1=n+1r by expressing nrand nr-1 in terms of factorials.

Q: Find an appropriate parametrization for the given piecewise-smooth curve in R³. x² + y² 4 16 C(t) =…

A:

Q: Given s(t) = 2t² a) v(t) + 2t, where s(t) is in feet and t is in seconds, find each of the…

A:

Q: Anthony Altino is mixing food for his young daughter and would like the meal to supply 1 gram of…

A:

Q: 6. Evaluate 1 √x²-9 1₂ dx.

A: here we have to find the integrals.

Q: Evaluate the limit (if it exists). Use L'Hospital's rule (if appropriate). 5 In x lim - 1 x→0 3x 5…

A:

Q: a. Find an equation of the tangent line at x = a. b. Use a graphing utility to graph the curve and…

A: Given:  y=ex; a=ln11 To Find:  (a) To find an equation of the tangent line at x=a. (b) By using a…

Q: Find the point(s) where a tangent line to the curve y = f(x) = 6x² has slope mtan = 48. The point(s)…

A:

Q: Classify each of the following equations as to order and degree: a. 3dy + (4xy - secx) dx = 0 b. L…

A:

Q: Find L-tan -¹ (7/²)

A: We are asked to find the inverse Laplace

Q: Find the limit. (If an answer does not exist, enter DNE.) VE+1² 2t - 1²

A: Given problem:- limt→∞t+t22t-t2

Q: The demand and supply functions for your college newspaper are, q = −9,000p + 2,800 and q = 3,000p +…

A:

Q: Find the absolute minimum and absolute maximum of on the closed triangular region with vertices…

A: Given f( x , y ) = 20 - 10x + 14y

Q: Find the derivative of the function at P in the direction of u. f(x, y) = In(9x + 4y), P(3, 9), u =…

A:

Q: The concentration of salt in a fluid at (x, y, z) is given by F(x, y, z) = 2x² + 2y² + 4x²x² mg/cm³.…

A: Given, the concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=2x2+2y4+4x2z2 mg/cm3. We…

Q: An open rectangular box has volume 48 cm³. What are the lengths of the edges giving the minimum…

A:

Q: Question 4 (i) Evaluate (Hint: Rationalize twice) lim x→2 19 √2x + 5 x 2 4

A:

Q: Find the derivative of the following function. 7x + 2 2 x² +7x+8 f(x)=

A: To find the derivative of given function

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A:

Q: A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The…

A: Given: A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour.…

Q: List the first five terms of the sequence. 2₁ = 6, an+1 = 2a + 3

A: Explanation of the answer is as follows

Q: Given f(x)=x²-13x + 48, find all values of x for which f(x) 28. The solution is (Type your answer in…

A:

Q: 12. y = e ², y=0, x=0, x=1

A:

Q: t Calculate the velocity and acceleration vectors and the speed of r(t) = ( √6 +²₁² ²1 1 6+1² (Use…

A:

Q: A 5-9 resistor and a variable resistor of resistance R are placed in parallel. The expression for…

A:

Q: et x and y be real numbers.   prove that if |x-y| < c, then |x| < |y|

A: Given : |x-y| &lt; c

Q: ). f(x) = √tan ¹x

A: Given query is to find the derivative of the function.

Q: Suppose you are climbing a hill whose shape is given by the equation z 900 0.005x2 0.01y2, where x,…

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

Q: 7. y sin x, y = π/2, x = 0; about y = 3

A:

Q: Venity Green's Theorem by evaluating both integrals √ √² dx + x² dy= [](ON-OM) A ax ay for the given…

A:

Q: Find the area of the region between the graphs of f(x) = 9x + 8 and g(x) = x² + 6x + 2 over [0, 2].…

A: From the given curves the bounded region is shown below. Now taking the vertical strip, so the area…

Q: 36. sin(x - y) = x COS (y + = ), ㅠ (37)

A:

Q: Find the differential of the function. z = x ln(y5 + 9) dr-([ dz = Need Help? [])ox + ay dx Read It

A:

Q: x² - 49 +8 dx

A: Topic:- application of integration

Q: Use the product rule to find the derivative. y = (5x² + 4)(4x - 5) y' =

A:

Q: he following. f(x, y) = 7e* sin(y) Find Vf(x, y). Vf(x, y) = Determine Vf(x, y) at the point(0, π…

A: Given: f(x,y) =7exsiny

Q: Evaluate the integral. 2 √(x - 5)²(x - 6)² (Use symbolic notation and fractions where needed. Use C…

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

Q: Suppose that you push a book across a 3-meter-long table by exerting force f(x) at each point from…

A:

Q: Find all the values of x where the tangent line is horizontal. 3 f(x)=2x³ +42x² +270x + 7 X=…

A:

Q: Show all work for the problems below. Use the given formula below. rth Term of a Binomial Expansion…

A:

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y² - 7z² where T is…

A:

Q: Suppose you are given an integral of the shape: cosxsinxdx, and you know that n is odd.

A:

Q: Use technology to sketch the level curve of f(x, y) = 4x - 2y + 9 that passes through P(1, 2) and…

A: Given: f(x, y)=4x-2y+9 Level curve passes through point P(1,2). The gradient vector at P=?

Q: Find the sum of the series below. Σ n=1 24η (2η – 1)2 (2n + 1)2 -

A: Answer: The solution is as given below:

Q: given the derivative g'(x)= x^2(9-3x)(x+4) find when the function g(x) has a horizontal tangent

A:

Q: If y = 2 sin (x), find the equation of the tangent line to the curve at x = Tangent line: NE

A:

Q: Consider the following polar curves: r = 1 cos 0 r = 1 - sin 0 (a) Find the points of intersection…

A:

Q: Find the points on the curve y = x4 - 12x2 + 3 where the tangent line is horizontal. y VN Solution…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: Find the slope of the tangent line to the parametric curve -4√2 X X = = 4 cos(t) y = 2 sin(t) at the…

A: