A log 10 m long is cut at 1-meter intervals and its cross-sectional areas A (at V= m3 x (m) A (m²) x (m) A (m²) 0 0.67 6 0.51 1 0.65 0.56 2 0.63 0.50 0.50 0.48 3 4 5 0.62 0.57 0.58 7 8 9 10

Q: Let f(t)=6t^2+8t. Estimate the following to within two decimal places by using small enough…

A:

Q: The population of a city can be modeled by P(t) = 20e0.00 thousand persons, where t is the number of…

A:

Q: (7) The shown graph below is the graph of function f. Note that the graph of f has local extrema at…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Use the indicated method of solution to determine a one-parameter family of solutions for each D…

A: The given differential equation is;  xy'=6y+12x4y2/3.

Q: Find first partial derivatives of (a) f(x, y) = x² + 3y + x³y² (b) f(x, y) = 2x² + 3x³y + 2x³y² (c)…

A:

Q: x= y^2 - 4y   x= y-y^2   find the area

A:

Q: 11. If h (2) = 8 and h' (2) = -5₁ Find d (h(x) dx x x=2

A:

Q: Consider the function f: [0, 3] → R defined by f(x) = sin(2x). A. Does the Mean Value Theorem apply…

A: Part (A) The mean value theorem is applicable to the function f if the f is continuous at the…

Q: Consider the following functions. f(x) = 7 − x2,    x ≥ 0;    g(x) =    7 − x  Show that f and g…

A:

Q: Graph f(x)=arctan(x) a) Describe the graph in words. What is always true about the graph of f(x) ?…

A: Solve as given below,

Q: 15. Obtain the differential equation of the family of straight lines through the point (5, 2).…

A: The given point is (5,2).

Q: if x -5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = I 5- Let…

A:

Q: 5. By variation of parameters, solve y" +4y = sin²x. Hint: You will have to apply some trigonometric…

A: We can solve this as follows:

Q: 22. A circle is growing, its radius increasing by 3 mm per second. Find the rate at which the area…

A:

Q: lim X→ 4x-3 lim x²+12x+27 ) lim x→-3 x+3 2x²-7x+5

A: (a)  given limit is :-limx→3412x2+11x-154x-3      00 form  since we know thaT  if…

Q: -5-4-3-2-1 3 2. 1 -3 1 2 3 5 y = f(x)

A:

Q: Solve the following problems completely. Show your graphical and analytical solutions. Express your…

A: 7

Q: state your understanding of the term ‘limits’

A: Limit is defines as a value that a function approaches the output for the given input values.

Q: If b₁ = a₂ in the equation (a,x+b₁y+c dx + (a₂x+b₂y+c₂)dy = 0, then the equat homogeneous. . For the…

A:

Q: 4. By method of undetermined coefficients, solve: y(4) - y(3) - y" - y - 2y = 8x³.

A: We have to solve differential equation y(4)-y(3)-y''-y'-2y=8x5by undertermined coefficients

Q: Sketch the graph of the following function. List the coordinates of where extrema or points of…

A:

Q: 1. Evaluate the following limits. nx 1 (₁ + ²) " (a) lim n→∞ (b) lim x →∞ (₁ + ²) ²

A:

Q: ²x = 1 + tan² x can x, sec² x dx dx integrals It is sim- (3) (4) (5) EXERCISES 8.3 Powers of Sines…

A:

Q: Solve in 20 min plz plz i need it

A: see below the answer and explanation

Q: At what point on the ellipsoid x² + y² + 4z² = 1 is the tangent plane parallel to the plane x + 2y +…

A: Given data:  ellipsoid x2+y2+4z2=1  Plane x+2y+z=1

Q: Q11 Compute the following limits: (a) lim (5-2x - x²) X--1 (b) lim x²+x-1 x-2- 2x+1 x²-2x x-2x²-3x+2…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 7. Study the convergence of the following series: (2) Σ 2n n² n=1

A:

Q: why are the position vectors of D, E, F (b+c)/2, (a+c)/2 ect and not D= (c-b)/2, E= (c-a)/2, F=…

A: The objective is to determine why are the position vectors of D, E, F are b+c2,a+c2, and…

Q: (2x²-x-y) dx-xdy=0; y(1) = 0

A: given differential equation is :-(2x2-x-y) dx-xdy = 0      ; y(1)=0cpmpair D.E  with Mdx+Ndy =0 here…

Q: Show all work and be at neat as possible. 1. A function f is defined as f(x) = 4x-5 x-8 a) State the…

A:

Q: Consider the function. f(x) = 4x³ - 12x² - 36x Step 2 of 2: Determine the open intervals on which…

A: Given query is to find the interval where function is increasing and decreasing.

Q: In 2000, 48% of the residents in a large city regularly used newspapers for getting news and this…

A:

Q: Let 3x3-y3 = 2. What is the value of dx/dt if dy/dt = -2 when x = 1?

A: To find the derivative of x with respect to t.

Q: Find the critical points of the function. (x, y, z) = f(x, y) = (5x − 2)² + (y - 9)² 50,2 X

A:

Q: Would you mind explaining why sub part a is incorrect? And could you please explain the solution of…

A: Here, we basically have 3 equations and 2 variables x and z.The 3 equations are:1 2z-6=72…

Q: Find equations of the tangent plane and the normal line to the given surface at the specified point.…

A:

Q: Suppose g, and h are functions satisfying 7 7 Sh ľ h(x) dx = 1, and g(x) dx - [² (3g(x) + h(x)) dx =…

A:

Q: Solve the equation for 0 ≤ 0 < 2π. Show all work.. = 4 + sin 0

A:

Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A:

Q: Question 3 Integrate: 1₂ 2x + 11 x² +8x+17 dx + C

A: Here we have to calculate the given integral. We have ∫2x+11x2+8x+17dx

Q: Estimating Slope In Exercises 9 and slope of the line.

A: here we have to find the slope of the line.

Q: Exercise: Graphing a Function with a Horizontal Shift PDF Transcript for Exercise: Graphing a…

A: 21. The given function is: rx=x-42 To graph the given function.

Q: Solve the following problems using either the Trapezoid Rule, or Simpson's Rule with N = 50…

A: Trapezoid rule, ∫abf(x)dx = △x2 {f(x0) + 2f(x1) + 2f(x2) + ... +2 f(xN-1) + f(xN)}where,△x = b-aNxi…

Q: Using Slope In Exercises 7 and 8, identify the line that has the indicated slope. 7. (a) m = 3/ (b)…

A:

Q: The polar curve r(0) = 1-20 is graphed for 0 ≤ 0 ≤ T. Let R be the region in the third quadrant…

A:

Q: Find the derivative of the function. f'(x) = X 1= √x+7 f(x) =

A:

Q: Find the volume formed by rotating the region enclosed by: x = 8.1y and y³ = x with y ≥ 0 about the…

A:

Q: Activity #3 1) A moving particle starts. ✓ (0) = (0,0,07 with acceleration It's is Find its Given…

A: 1. The given data is: at=4t i+6t j+k Initial condition: r0=0, 0, 0V0=i-j+k

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A:

Q: Find the limit of the following expression: lim (a) f(x) = = (c) 2 (a) DNE (b) 0 For what value of x…

A: