Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the point(s) of inflection(s) of f(x) and the interval(s) where f(x) concaves up and concaves down

Q: X-1 4 = = 2 – y = z 2 y-2 z-1 12 = x = -1, 3 2 Show that these are skew lines.

A: To show that the given lines are skew lines.

Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 3s2+5s+1 (d) 3…

A:

Q: In Problems 19-36 use Theorem 7.1.1 to find L{f(1)}. 19. f) = 21* 20. f(1) = r° 21. f(1) = 41 - 10…

A: Laplace transform

Q: 6s-4 82-4s+20 2et cos 4t + 8et sin4t None of the Choices Option 2 2e 2t cos 4t + 8e-24 sin4t 6e 24…

A:

Q: 3 c2x S *x² dy dx 4.

A: Integral

Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

A: sum of number is 23 let a number = x  other number is 23 - x

Q: 15. What are the coordinates of the vertices of the ellipse A. (-6,0) and (6,0) B. (0, -6) and (0,…

A: 15  y2/9 + x2/36 = 1 compare with x2/a2 + y2/b2 = 1 so a = + 6     b = + 3 so here vertices  (a,0)…

Q: if f'f′ is the derivativeof ff with 2∫1f'(x)dx=10∫12f′(x)dx=10 and f(2)=4,f(2)=4, then f(1)

A:

Q: 2. The number, N, of bacteria in a culture at time t, in hours, is N(t) = 1000[30 + e a. What is the…

A: Topic:- exponential function  Note:- as per our guideline if more than three subparts posted than…

Q: f (x+h)-(f(x) 7. In finding the limits of the difference quotient ,on what value does k approach? a)…

A:

Q: Consider the function f(x) = The value of f'(0) is: (x+ 1)2

A:

Q: iSy dx dy 3.

A:

Q: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: a²z B. For each of the following functions z, find a² z and ду? a² z дх? дудх" дхду" 1. z = 2x2 –…

A:

Q: III. GRAPH ANALYSIS: The graph of f is shown below. Use it to answer A, B, and C. -7 -$ -4 -3 -2 1 2…

A:

Q: '9 — х? dx x2

A:

Q: i need the answer quickly

A:

Q: tan () (9) sin (4) F. Evaluate the integral r2 cos ()

A: integration

Q: Q2 The following graph shows the position function r(t) of a mass attached to a spring. Note that…

A:

Q: Use (a) bisection method and (b) false position method to find the solution to the following within…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

Q: (3t — х)е-2t | Given : v = Find ar2

A:

Q: 6x? + Sx t 16 dx +2x +6 x + 3? a.Sinlat3l+; 4 Cが)返が)+c er none

A:

Q: Find y=f(x) if f''(x)=4x^2, f'(0)=3, and f(0)=2.

A:

Q: Directions: Determine the reasons of the following statement In the given figure, if EF GH, then EG=…

A: We want to identify the steps.

Q: 13. Use a polar integral to find the area of the region defined by - Cos 0 KA<T

A:

Q: #2

A: To find out the integration.

Q: Calculus How many numbers are relatively prime to the following number. - 209 - 323 - 867 - 31…

A:

Q: Let N1 (h) be the approximation of f'(xo) with some numerical differentiation scheme depending on h.…

A:

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

A:

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: Use Method of Variation of Parameters: [D² - 8D + 16]y = e4Xsec2x

A:

Q: Determine the local maximum and minimum values and the saddle points of the function: f(x,y)…

A: Given, f(x,y) = y3 + 3x2y - 6x2 - 6y2 + 2

Q: dx 8. Evaluate the integral / zlnrV(In x)² – 8 x In a V(In a)2 – 8 |

A:

Q: Find an implicit and an explicit solution of the given initial-value problem. dy y – 1 dx x? - 1'…

A:

Q: 4s + 12 s2 + 8s + 10 4e -4t – 4te -4t 4e4 + 4te4t Option 3 Option 2 -4t 4e + 4te¬4t

A:

Q: Volume of Solid Revolution(Circular Disk/ Washer Method) Find the volume of the solid generated by…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

Q: Evaluate the limit x2+19x- 48 lim x--3 x2-11x+42 O a. а. 0 b. None of these. С. 13 11 d. 00 е. 13 17

A: Limits

Q: d of Variation of Parameters: [D² - 8D + 16]y = e4%sec2 %3D

A:

Q: 4. Determine the equation of the plane passing through the point (1,-4, 3) and parallel to the plane…

A: Explanation of the answer is as follows

Q: Find the differential dy: y = In (sec2 (3* )). -2a+5 O tan (3-2+* ) dæ -2r+5 dy = (x – 1)…

A:

Q: dy Find dx y = = 5x° sin x coS X

A:

Q: 11. A spherical balloon is inflated so that its radius (r) increases at a rate of (2/r) cm/sec. How…

A:

Q: 2 sinh x Calculate the integral, J dx. 5+ 6 cosh x

A: Given :∫2sinhx5+6coshxdx

Q: 2. For the parametric equation shown below, determine the value of (dyldx) and (d²y/dx?). x = 3t? –…

A: To find dydx&amp; d2ydx2 using the given parametric equations.

Q: 1. lim (6x + 1)cotx

A:

Q: 1 X• In( coS lim (* - In(cos )) x00

A: Given

Q: 3s – 14 - s2 – 4s + 8 - 3e2t cos 2t + 4e" sin2t 3et cos 2t – 4eª sin2t Option 1 Option 2 4e" cos 2t…

A: Given: Fs=3s-14s2-4s+8   As we know that; The inverse Laplace transform identity. 1).…

Q: Find the center and radius of the sphere. 2 2 5x + 5y + 5z + x +y +z = 16 Center = (OOD. radius = 4…

A:

Q: Consider and know that the function g defined by 1 g(x, y) = cos (TX /y) + log3(x – y) Answer the…

A: