Which of the following is the graph of y= sin (3x) for 0 ≤ x ≤ 6m?

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: here is the solution:

Q: The arc length of a given function is determined by √1+f'(2) dz Find the length of f(x)= (2/3)…

A:

Q: 1. 9x2 + 4y2 = 36 2.222² 쫑 = 1

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that…

A:

Q: (a) Find the derivative of ƒ (2) = (x² + 5) (8æ — 5) by first expanding the polynomials. Enter the…

A: We have to find out derivative

Q: f(x)= x/pi + pi/2+ pi/x + 2/pi Find the derivative

A: Let f(x)= x+a, a is a constant So, f'(x)=1

Q: Find the area between the curves. 1/5 6/5 y=x, y = 4x ... The area between the curves is (Do not…

A:

Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: A circular plate is submerged in a water of weight density (pg) 9810 N/m³. If the total force on the…

A: the answer is given in step2

Q: Find the Laplace Transform of f(t) = sin2tcost (A) B 2 s+55² +4 2 E s² +3 s+10s² +9. +(57+55²+4) Ⓒ4…

A:

Q: 7. dx S- X-3√x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the radius of convergence and interval of convergence of the series n=1 (x - 5) n n5n

A: Radius and interval of convergence

Q: Consider the following differential equation to be solved by variation of parameters. y" + y =…

A:

Q: Evaluate the limit lim_ (8x² + 4) (6x + 8 →7

A:

Q: 3 Find the Cartesian coordinates of the following points (given in polar coordinates): 3.a (√2, π/4)…

A:

Q: Give the order and degree of the following differential equations. Differential Equation 2 (d²y) dy…

A: Answer and explanation is given below...

Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

A:

Q: Find the limit as k approaches infinity for k ^(1/k)

A: Topic:- calculus

Q: Solve the initial value problem by Laplace y" +4y=20 e y(0)=3, y'(0) - 12

A:

Q: What is the difference between Rolle's Theorem and The Mean Value Theorem? Explain

A: See the details solution in below

Q: Let R be the region below the curve y = 4x², to the left of above the x-axis. Find the centroid of…

A:

Q: b y' = 2 + ₁e-ax a

A: details steps are given in step 2

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

A:

Q: The approximate rate of change in the number (in billions) of monthly text messages is given by the…

A:

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

A:

Q: -1 Range of f -4 -5 -6 O (c) Describe the relationship between the graphs. Domain of 1 -81 Range of…

A:

Q: Problem 2.7 Let Find the limit lim f(x). x 0 f(x) = x² if x is rational 0 if x is irrational.

A:

Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

A:

Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

A:

Q: Complete the description of the piecewise function graphed below. 6 5 4 4 if m-fi { f(x) = -2 if 3…

A:

Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

A:

Q: el For the function z = f(x,y) = - 4x³ -6y² - 7xy, find t V ne ON dz dx dz 3x forr || f(-5,4)=…

A: The given function is: z=fx,y=-4x3-6y2-7xy   As we know that; The Power Law: ddxxn=nxn-1

Q: 14) At what point on the graph of f(x) = instantaneous rate of change? a. x=8, x=2 b. x = 4 2009-2…

A: Given fx=x-8x-2x-4

Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

A:

Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: Use Properties of Exponents and Properties of Logarithms to simplify and the following expression…

A:

Q: Match the differential equations and the description/s that is/ are true to the differential…

A:

Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) =

A: Given y''+y=csc(x) Complementary solution: We will solve this equation by variation of parameters…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y² + z² (8,…

A:

Q: Use the maximum magnitude of the remainder term to find the maximum error in the following…

A:

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

A:

Q: a B sin(A) = cos (A) = Note: Triangle may not be drawn to scale. Suppose a = 9 and b = 2. Find an…

A:

Q: The integrating factor of the given DE are already given below. What is the value of “n” y2dx…

A:

Q: Using the circular disk method, find the volume of the solid generated by revolving about the…

A: Given curves , y=x ,                   (1)x=4.                       (2)

Q: O O O O O IfE is the solid hemisphere a² + y² +2²5 49 and y 20, set up the integral using spherical…

A: Solution: In converting to spherical coordinates, we use so that

Q: For the function, do the following. f(x) = 1/x from a = 1 to b = 4. (a) Approximate the…

A: The function fx=1x from a=1 to b=4

Q: Find the gradient of the function at the given point. Function f(x, y) = x² Point (4,4) Vf(4,4) = x²…

A: In this question we have to find the gradient of the function. Note: As per our policy we can solve…

Q: Find the general solution of the given higher-order differential equation. d'u 분 700분 - 20분 +7. dr5…

A: The given differential equation, d5udr5+7d4udr4-2d3udr3-14d2udr2+dudr+7u=0

Q: 10. 2ste tds +(s²e-t - t)dt = 0

A: