Find the general solution for the following equation: y''' + 3y'' – 4y' – 12y = 0

Q: Find the dimensions of a rectangle with area 216 m whose perimeter is as small as possible. (If both…

A:

Q: -Ihd the x-values of all points where the function has any relative extrema. Find the value(s) of…

A: f(x)=-103x3-512x2-5x+19f'(x)=-3×103x2-51×22x-5⇒f'(x)=-10x2-51x-5f'(x)=0⇒10x2+51x+5=0By quadratic…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 4, 5) (b)…

A:

Q: Select from multiple choice and fill in the blanks

A:

Q: 4. V40-4v-v² dv – 4v

A: This question can be solved by using the concept of some special integrals.

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A:

Q: Given the following vectors, add the vectors and find the magnitude and angle of the resultant…

A: 4. Given, v=(5,9) u=(-5,-9) According to given, Resultant(R)=((5-5)²+(9-9)²)1/2 R=0 Angle is given…

Q: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. 1 y…

A:

Q: 9/ Evaluate (cos* 0 – sin* 0)de T/12

A: Note that: cos4θ-sin4θ=(cos2θ-sin2θ)(cos2θ+sin2θ)=(cos 2θ)(1)=cos 2θ

Q: 3dt 1. (2t+8) Vt+1

A:

Q: Find the Gauss quadrature rule for f(x)dx z wof(xo) + wif(x1) + wzf(x2). Nodes: Xo = X1 = X2 =…

A:

Q: Evaluate ſV7– x²dx

A:

Q: S cor* (***) csc (*) da 3x+1) 3 3x+1

A: Solution…

Q: Consider the figures below. (1) (2) 5- 4. Use the rectangles in each graph to approximate the area…

A: Solution is here

Q: dy Find and simplify whenever possible. dx secx+tanx 1. y sec x-tan х

A:

Q: 4. V40-4v-v dv

A:

Q: 2xydx+(x^2)dy=0

A:

Q: Find a positive number such that the sum of the number and its reciprocal is as small as possible

A: Second Derivative Test :   Firstly find critical point of f(x).i.e, f'(x)=0 and find the value of…

Q: Decide if a direct comparison test can be used to determine convergence of the following series.…

A:

Q: direction as the vector from the point ?=(0,3) to the point ?=(−2,−2)?

A: Given query is to find indicated vector.

Q: 2. Find the equation of tangent line and normal line to 3x y3 + 2y =1 at (0.2) (15 points)

A:

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

A:

Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X00 X-00 -5 + 2e-* f(x)…

A: The objective is to evaluate the limit.

Q: ds Find the function s(t) satisfying = 4 -9 cos t and s(0) = 7. dt

A:

Q: x²+1, xs1 f (x) dx if f (x) = 2, raluate x> 1 A) 10 20 B 3 12 8 D 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: af Given f(x, y) = In(6x² + 8y²) then %3D

A:

Q: Find dx and simplify whenever possible. 1-cosh x 1. у 3D 1+cosh x 2. y = x tanh¯x + In V1 – x²

A:

Q: dx 11 J V64x2 - 121 8 11 18 – In-x+ 8 3 A +C 64x2 – 121 B In 1 V64x2 - 121 +C 11 In V64x2 - 121 +C…

A:

Q: QUESTION 16 Larger standard error of an estimated parameter will lead to narrower confidence…

A: Given statement is Larger standard error of an estimated parameter will lead to narrower confidence…

Q: 345 cos dx 1-cos24x+sin? 4x

A:

Q: Find the value of x for which the value of the function f(x) = x +3x2 - 2 is minimum? %3D Answer:…

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 u · (v x w)| to determine…

A:

Q: 2. Vy-2+1 dy

A: ∫vn dv = vn+1n+1+C

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

A:

Q: Suppose the position of a particle is given by parametric equations x(t) = t3-3 and y(t) = 2t2. (a)…

A: Solution: x(t)=t3-3  and y(t) = 2t2

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that  required plane passes through point ( 7, 6 , 6 )  and perpendicular to the vector having…

Q: 3dt 1. J (2r+8) fr+1 Suv-2+1 ¢v 25x -9 dx 3. 4. V40-4v-v dv

A:

Q: Consider the function y = 3x2+2x-4. What is the exact value of C in the interval [-2, 4] such that…

A:

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

A:

Q: Suppose that enrolment in CLSU has been increasing over the years since year 2014 according to the…

A:

Q: is given by: If f(x, y) then 8(8x-4y) '

A:

Q: A student throws a ball upward from a height of 48 feet, initially at 32 ft/sec. The function that…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an…

A: Explanation of the answer is as follows

Q: f(x + Ax) - f(x) Find lim Ax-0 Ax f(x) = 3x- 9x %3D Step 1 Find f(x + Ax) by substituting x + Ax in…

A:

Q: e" + e¯ cosh(r) : e - e sinh(r) 2 Use our rules for differentiating e" to show that cosh'(r) =…

A:

Q: Choose the correct speed and direction of a plane with a velocity of (-5,12) . 13,293° 17,113°…

A: Find your answer below

Q: Given than | f(x) dæ = 4 and f (x) da 8, which of the 3 following is NOT TRUE?

A:

Q: Consider the parametric equations below. x = 5t - 4, y = 4t + 2 (a) Sketch the curve by using the…

A: Consider the parametric equation  x=5t-4,  y=4t+2

Q: Find the dot product of v and u and determine if the vectors are orthogonal. a. v = , u = The…

A: There is more than 1 question, as per the Q&A guidelines we are answering the 1st question. If…

Q: S4tan3 (пх + 1)dx

A: ∫ 4tan3πx+1dx=4·∫tan3πx+1dxLet u=πx+1.=4·∫tan3u1πdu=4·1π·∫tan3udu=4·1π·∫-1+sec2utanuduLet…