A smooth curve C is defined by some vector function R(t) with R (7) 2 = = (π,0,−2) and R' (t) = (2, √5 csc t, 2 cot t) for all t € (0, π).

Q: Onsider the function f(x) = -4x²+7x+6. Interpret the e average rate of change from x = -7 to x = 7…

A: Topic:- application of calculus        Definition :-  The tangent represents the instantaneous rate…

Q: 5. S √x²-a² dx

A:

Q: Given f(x) X-4 O[-4, 12) u (12,⁰0) 01-4,00) and gxx)=√x+4, what is the domain of f(g(x))? 0 (-∞0, 4)…

A: This question can be solved using the concept of domain of a function.

Q: What is the equation of the rational function g(x) and its corresponding slant asy -10-9-8 O O O 7…

A: Given: Graph:

Q: Find the transfer function, G(s)=C(s)/R(s), corresponding to the differential equation, d³c dt3 +30²…

A:

Q: Find equations of all tangents to the curve f(x) = 4/x that have slope -1. Options attatched

A: f(x) = 4/x                    Slope of tangent = -1

Q: Which of the following equations represents the nth term of the arithmetic sequence? 17, 24, 31, 38,…

A:

Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

A:

Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

A:

Q: The magnitude of the vectors and are 6 and 10 respectively, and the angle between them is 45°.…

A: The equation of the vector dot product is A⋅B=|A||B|cosθ, where θ is the angle between the vectors A…

Q: Given that answer = [*f(x) dx = 45 13 > [². what is f(v)dv?

A:

Q: "풍 2 secx dx tan³x + 4 tanx

A:

Q: Find y′′ y = -3x4(4x+6)2

A: Recall: Power rule; dxndx=nxn-1 Given, y = -3x4(4x+6)2

Q: The angle between the vectors √2 – 1,√2+1, √2] and [1,1, 1] is: 60° 45° 30° 90°

A: Given vectors are :  [2-1,2+1,2]   and  [1,1,1]   Let,  a=[2-1,2+1,2]   and  b=[1,1,1] The angle…

Q: •+∞0 4-1² 1 x² + 4x² dx

A:

Q: 5. S (2x²+1) x3-3x+2 dx

A: Here we have to find the integral.

Q: A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7…

A:

Q: 5.5x³(a²-x²) ²/dx

A: The given problem is solved below in detail.

Q: 1-y 2 Consider the plane : x - 2y + 3z - 1 = 0 and the line 1: x= 1. Find the point of intersection…

A: 1) Given: l: x=1−y2=z+1 Let ,  x=1−y2=z+1 = λ Any general point on the line l will be x=λ, y=1-2λ,…

Q: Which of the following graphs represents (x-2)² + (y+4)² = 257 1. le - 4 - 7 . $ 4 2 2 2

A:

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A:

Q: 2. Sketch the solution region of 2x − y − 1 > 0 (x − 5)² + (y + 1)² ≤ 25.

A:

Q: IV. Fill in the blank to make each statement true. Use correct notations. 12π ¹ (sin ¹25). = 1.…

A: We can solve this as follows:

Q: 1 The limit is 0 and the function is continuous at the point. The limit is 0 and the function is not…

A:

Q: 23 14 f(x)dx – ¹ f(x)dx - - where a = = b [ f( and b = f(x) dx

A:

Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors x+8 x+8 x²+x-2…

A:

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

A:

Q: the

A:

Q: Consider the function f(x) = (4 - 5x)7. Find the second derivative f"

A:

Q: Determine the interval of convergence of n=1 (x - 5)" n²

A:

Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: If f(x) = 1- log5 , then f-¹(x) =

A: Given that a function f(x)= 1 - log5x and we find f-1(x) .   Here i attached the solution of this…

Q: 4. S dy y³-2y²

A:

Q: Set-up the definite integral that will give the measure of surface area of the solid generated 1 by…

A:

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: Which of the following polynomials has an odd degree and a positive leading coefficient? W O -10-947…

A:

Q: Find an equation for the hyperbola described. Graph the equation Center at (-5,-4); focus at…

A: We need to find equation of hyperbola.

Q: 6. (y -x + xy cot x) dx + x dy = 0 Answer: xy sin x = C + sin x - x cos. x.

A: We have to solve this question with exact formulation.

Q: D Question 24 Suppose that P= f(t) is the population (in millions) of the country & years after the…

A: We can find the answer as below.

Q: Jacob's father is planning to open a savings account to pay for Jacob's college education. He has…

A:

Q: 2. √a²-x² dx x2

A:

Q: Find the derivative of the function f(x) = e8+5x³. O f'(x) = 8+52³ O f'(x) = (8 +5x³) e³+5x³ O f'(x)…

A: To find derivative f'(x)

Q: Which linear equation is shown below? y = x/5 +2 y = 4x + 3 y = 5x + 2 y = 5x - 2 y = 5x + 4

A: To find out the correct linear equation which is shown in the graph below.

Q: Find the equation of the tangent plane to z = ln(x³ + 1) + y³ at the point (0,6,216).

A:

Q: The sequence is given. Part A: Assuming the pattern continues, list the next four terms in the…

A: We have to find the solution .

Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d d.x 10 t³ dt =

A:

Q: The graph of a function h is given. domain -6-5-4 -3 -2 range y 5 (a) Find h(-2), h(0), h(2), and…

A: As per guidelines we can answer only three subpart questions at a time so if you need more answers…

Q: Consider the graph y = f(x) below. -4 -3 -2 3 2 tion 8 6 2 3 T Find all value(s) of a such that lim…

A: The objective of the question is determine the points in which limits doesn't exist and not…

Q: The critical numbers r = -1 and x = 2 are found from a continuous derivative f(x). Given that the…

A: