(2) The population of the world in 1995 was about 5.7 billion, and the estimated relative growth rate is 2% per year. If the population continue to grow at this rate. (a) Express the population in term of the number of years t after 1995 and estimate the population of the world in 2012; (b) By what year will the population have doubled? When will it have tripled?

Q: Find the slope of the tangent line to the graph of X = 13 15 x2 at the point where V y = x For the…

A:

Q: Find the volume of the solid generated when the region bounded by the graphs o y = x, y = 0 and x =…

A:

Q: lim 2 76. Sketch a graph of a function with the following properties: f(x) = 1. f(x) = 3. f(x) = 6,…

A:

Q: Find all points of intersection between the curves. r = v √3 cos (30) and r = sin (30). Enter your…

A: Given that:r= √3 cos(3θ)  and  r = sin(3θ).  Find all points of intersection between these curve.

Q: Find the tangential and normal components of the acceleration vector. r(t) = (3t – t³) i + 3t² j O…

A: Take derivative.Find the magnitude.

Q: use implicit differentiation if applicable show proof (complete solution) y=e(x+c) is a solution of…

A: The given equation is

Q: Find the area A of the shape bounded by the x-axis, the function y = ei and the lines x = 3, x = 6.…

A:

Q: In Problems 5 and 6, compute y' and y" and then combine these derivatives with y as a linear second-…

A:

Q: The height of a bottle rocket, in meters, is given by h(t) = −3t² +47t + 600, where t is measured in…

A:

Q: lim x 2 X- 1 x² 2 1 4 The limit exists, lim x 2 The limit does not exist x - 2 1 1 x² 4 - ||

A:

Q: The improper integral S integral $ 55 d dx - 3 (x-3)² (a) is indeterminate (b) diverges to +∞o (c)…

A: We use substitution method to solve the integral.

Q: Simplify sinh (4 In (3x)).

A: To simplify the expression sinh⁡(4ln⁡(3x)),We can use the properties of hyperbolic trigonometric…

Q: Classify each of the following ordinary differential equations by stating the order, determining if…

A: Order of differential equation: It is defined as the highest order derivative the differential…

Q: Use calculus to derive the volume of the unit sphere.

A: Use calculus to derive the volume of the unit sphere.

Q: Evaluate π -T π S f(x) dx, where f(x) dx = f(x) = √4x³, 3 sin(x), -π≤ x < 0 0≤x≤T.

A:

Q: dy d.x x-1 2, y(0) = 1.

A: Here we will solve the given differential equation by variable separable method

Q: 2. Solve each equation (round answers to four decimal places if needed A. log(x+4) + log(x+3) = 1 B.…

A:

Q: 14. Consider the plane 3x - 4y + z = 2 and the point P = (1, 2, -1). Find the point of intersection…

A: Given that, the equation of the plane is    and the point

Q: where the function f(x) = 2x² - 16x³ - 126x² +9 is increasing and where it is decreasing. tion start…

A: In this question, we will find the interval of increasing and decreasing.

Q: (e) Sex ex cos x dx x³ In x dx (d) (f) [x sec² x dx

A:

Q: Consider the following. x = e4t y = t + 11 (a) Eliminate the parameter to find a Cartesian equation…

A: we have given set of parametric equation

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x³9x² - 21x + 8 (a)…

A:

Q: 1. Points P(1, 1) and Q(x, y) are on the graph of the function f(x) = x³ Complete the following…

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: Video Example Find the critical numbers of the function. f(x) = x³/5(7 - x) Solution First note that…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: Part a) Given the graph of f(z) below, evaluate each of the following limits. 8 7 6 5 4-3-2 lim f(x)…

A: given graph of function to find the limits

Q: Ben​ Franklin's gift of ​$9​,000 to New York City grew to ​$8​,000,000 in 200 years. At what…

A: The compound interest formula for the final amount when principal amount is compounded annually is…

Q: 1 2. v = (-9, 2) is transformed using the transformation matrix A = H What is the resulting vector?…

A:

Q: Q4/ Find the directional derivative of the function F(x,y,z)=x+xcosz-ysinz+y at the point P.(2,-1,0)…

A: The given function is; F(x,y,z)=x+xcosz-ysinz+y

Q: For the points P₁(-5,3,2) and P2(2,1,0), find the direction of P₁ P2 and the midpoint of line…

A: To find the direction and midpoint.

Q: Determine the interval(s) on which the following function is continuous, then analyze the given…

A: H(x) =(2+2sinx )/(cosx).

Q: Using the definition, calculate the derivative of the function. Then find the values of the…

A:

Q: Find three mutually orthogonal unit vectors in R³ besides ±i, ±j, and ±k. There are multiple ways to…

A: Assumed vectors:The unit vectors are the vectors whose magnitude is 1.Assumed vector u is not an…

Q: Find the arc length (8) of the curve (t) 8 F(t) = (-4t - 4, 2t³/26, 4³/2 - 5) for 1 < t < 3 = 11

A: given paratmetric curve to find arc length

Q: A sample of radioactive material disintegrates from 5 to 4 grams in 200 days. After how many days…

A:

Q: Let g(x) - [₁6'd -3 g'(x) = -0 6t²dt. Find g'(x).

A:

Q: -2pi Find a formula for the graph of the function y = f(x) given in the figure above. Y 6 8 2pi

A: We have to find a formula for the graph of the function y = f(x) given in the figure.

Q: A company tracking its profits notices that the relationship between the number of items sold, x,…

A: Let a line is passing through two points  Then slope of the line is given as follows

Q: A right-circular cylindrical tank of height 8 ft and radius 4 ft is laying horizontally and is full…

A:

Q: 2 x-3 Find the slope of the secant line on the graph of f(x) for each interval: Let f(x) =

A: given function

Q: Determine whether the function shown below is a​ one-to-one function. If it is​ one-to-one, find its…

A:

Q: Find the equilibrium price and quantity for the following supply and demand functions. Demand: p =…

A:

Q: Let f(x) = (6 - x - x² if x≤ 4 2x - 9 if x > 4

A: f(x)={6−x−x2 if x≤42x−9 if x&gt;4

Q: Let an (a) (3x-3)n 3n+3 (a) What is the ratio In this question we consider the interval of…

A:

Q: Determine whether the equation is exact. If it is, then solve it. 5y cos (xy) + 1 g 2 dx + 5x cos…

A: d(xy) = x dy + y dx

Q: The graph of a function is given to the right. Use the graph to find each of the following. a. The…

A:

Q: 1/3 At what points is the function y = (5x-4) continuous? Describe the set of x-values where the…

A: given function

Q: Find the gradient of the function at the given point. f(x, y) = 3x + 4y² + 2, (3, 1) Vf(3, 1) = = X

A:

Q: The point P(1, 1/5) lies on the curve y = x/(4 + x). If Q is the point (x, x/(4 + x)), use a…

A:

Q: Find the unit normal vector N to r(t) = (t, cos(t)) at t = 34. (Use symbolic notation and fractions…

A: Find the unit normal vector  to  at .