1. Given ā = 31 -9j and b = -6i +j compute each of the following. (a) 105 (b) 14ā + 205 1 (c) 8b 3

Q: Find T(t) and N(t) at the given point. e' cos t, y = e' sin t, z = e'; t = 0 %3D T(0) %3D N(0) = %3D

A: Given vector x=etcost, y=etsint, z=etr→(t)=<etcost, etsint, et>

Q: 1. Sket dh the graph of the cylinder r = (y – 2)2 in R. %3D

A:

Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

A:

Q: f(x) = In(x4 + 1)

A:

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A:

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 & h=0.002

Q: Find the relative maximum and minimum values and the saddle points. f(x.y) = 242y +x -xy

A: Using D=rt-s^2 If D >0 and r>0 then relative minima and r <0 then relative maxima  And at…

Q: Find the slope of the tangent line to the curve y = (1+ 4x)7 at the point x = 2. %3D

A: Slope of the tangent line is obtained by just derivative of the function  wrt the independent…

Q: Find the area (to three decimal places) bounded byf(x)=x^2e^x and q(x)=4-x^2

A: Given problem:- Find the area (to three decimal places) bounded byf(x)=x2 ex and q(x)=4-x2

Q: Set up the definite integral required to find the area of the region between the graph of y = 15 - =…

A:

Q: Question 16 Use a triple integral to find the volume of the solid. The solid bounded by the surface…

A:

Q: Evaluate the limit. 12 lim x-5 x2 + 2x – 35 5 Give your answer in exact form. If the limit does not…

A: topic - limits

Q: Evaluate the iterated integral. 1 2r y 8ry: dz dy dx

A:

Q: Using appropriate substitution dx 4 (x+ 1)2 - is equal to -/4-(x+1)2 – sin- (*) + C the above…

A: Given problem:-

Q: Determine whether the following function is a polynomial function. If the function is a polynomial…

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A:

Q: Use a double integral to find the volume of the indicated solid. 9 z = 9–2 y 2 y=2 4 X=4

A: Consider the solid

Q: 6 6 iwen ["r*dz = 320, x³ dx x dx 16, dx = 4, evaluate the following using properties of definite…

A:

Q: Find all the values of x between 0 and ë where the tangent line to the graph of y = sin (x) cos (x)…

A: We will use the concept of differentiation to solve this.

Q: Consider the expression: ey = 4x + y* , In which y is an implicit function of x , after derivation…

A: Given problem :- ey =4x+y4 , find y'

Q: combination lock will open when you select the right choice of three numbers (from 1 to 30,…

A:

Q: 40senz are solutions of the differential equation senr It's known that y1(x) 2(z) : 4z2y" + 4ry' +…

A:

Q: How can we write out the summation of this notation

A: Topic:- simplification

Q: The value of the integral I = is required in the development of the normal probability density…

A:

Q: aluate the iterated integral. || 5x²sin(y) dy dz dx =

A: Given: ∫0π∫05x∫0xz5x2sinydydzdx

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: Each unit of a product can be made on either machine A or machine B. The nature of the machines…

A: Here, from the given details, C(x,y)=30+x26+260+y39 That should be minimized using…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. da dz dy = y -54 J-36 %3D

A:

Q: Determine the derivative of y. y = ev12x+8 %D

A:

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: gths of pregnancies in a small rural village are normally distributed with a mean of s and a…

A: Here the range is 233to 293.  Here I am providing my notes

Q: Find the area of the region enclosed by the rose r = 18 cos 30. NOTE: Enter the exact answer. A = T

A:

Q: In every sphere of radius r it is true that its volume V is given by V =ar³ , A snowball is melting…

A: volume of snowball (sphere);V=43πr3differentiating w.r.t. time t;dVdt=-4π3(3r2) drdtdVdt=-4πr2…

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

A:

Q: Find the volume of a cap of a sphere with radius 50 and height h = 3.

A: volume of sherical cap with radius given r=50 and height=3

Q: Prove 2^1/n infinity n=1 is convergent

A:

Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

A:

Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 & x2=8

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A:

Q: A combination lock will open when you select the right choice of four numbers (from 1 to 45,…

A: Topic = Algebra

Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 4 1 lim 5t2 + 6 7t (?,?)

A:

Q: Find the centroid of the region bounded by the graphs of 512 y = x, x = and y = 16. NOTE: Enter the…

A: Given; y=x , x=512/y^2 , and y=16

Q: Perform the indicated operation. Simplify if possible. b2 64 b+8 b+8

A: To simplify the given expression.

Q: 2 Find the Inverse Laplace transform f(t) if given the Laplace Transform function 1 F(s) = using…

A: Use partial fraction

Q: The current population of a certain bacteria is 5410 organisms. It is believed that bacteria's…

A: Given, Initial population (P)=5410 , Rate of multiples (R)=3 , Triplet in 9 minutes. Therefore n=9…

Q: alculate D(f ◦ g) for the fun

A: answer is in next step

Q: 4. Show that a b a +

A:

Q: y = 6x³ – x-4

A:

Q: 3.1 If the Laplace transform of coswt is then find the Laplace Transform of the s2+w? following…

A:

Q: A test program for grade 10 can generate quadratic functions in a standard form y = ax + bx + c…

A: