Calculate r' (t), T(t), and T(2) where r' (t) = {| T(t) = ( T(2) = ( 9 r(t) = (2t², 2t¹).

Q: 2) f(x) ㅗ X

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: √1-y² dx - √√1 - x² dy = 0, y(0) : V 3 = = 2

A:

Q: Give the largest interval I over which the solution is defined

A: Solution is giventhe largest interval I over which the solution is defined

Q: If r(t) = i +tj + t²k,

A: r(t)=i+tj+t2kUsing the power Ruleddxxn=nxn−1

Q: Q3/ Find the area of the region enclosed by the parabola y=x²-2 and the line y = 2. f flor تر 1

A:

Q: Use the even-odd and periodic properties of the trigonometric functions to simplify. -4 sec (-t+2)…

A:

Q: Prime number

A: To find:Define the porime numbers

Q: Yaster Car Sharing offers a membership plan with a $54 per month fee that includes 13 hours of…

A: Here, car Sharing Yaster Car Sharing offers a membership plan with a per month fee that includes…

Q: Revenue The revenue (in dollars) from the sale of a infant car seats is given by R(x) = 70x -0.02x²,…

A: The objective of this question is to find the instantaneous rate of change of revenue at a…

Q: Part 3: Explain a. Differentiate the following function(s) using the chain rule. b. Then,…

A: Chain rule:

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

A:

Q: Solve the initial value problem. ( + 16y²x) dx + (16yx² - X dx + (16yx² - sec²y) dy= 0, y(1) = The…

A:

Q: Problem 104. The residents of Raytown are dealing with an epidemic of Creeping Crud. The first…

A:

Q: dy dx a- 2e2y = ln x² b- y = (lnx+x)tanx d- y = ln xex 4) Find

A:

Q: 1. If y-4 = √x+2 c) Using interval notation, find the domain and range of the function.

A:

Q: Graph A AN f(-2) =-2 lim_ f(z) =3 lim_ f(z) = [1] lim f(z) DNE Graph C f(-2)=0 _lim_f(z) = lim_ f(z)…

A: The left hand limit of a function f(x) is the value of the function approaches when the variable…

Q: Suppose that the average cost, in dollars, of producing a shipment of a certain product is C= 5,000x…

A:

Q: Problem 116. Justo has a twelve-foot ladder leaning against a vertical wall as shown below. Mr.…

A: We need to find the value of .

Q: Find fo g, go f, and go g. f(x) = x², g(x) = x − 1 (a) fog (b) gof (c) gog

A: The objective of this question is to find the composite functions f(g(x)), g(f(x)), and g(g(x))…

Q: f(x): -x+4, -x+3, -3, f(-6) = lim f(x) = lim_ f(x)= 2+6+ lim f(x) x < -6 -6 ≤x≤4 f(4) = lim f(x)=…

A:

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 100e−x2 − 5y2 − 7z2 where T is…

A: T(x,y,z)=100 e-x2-5yz-7z2 is the given equation and we have to findrate of change of temperature…

Q: The table shows speedometer readings at 10-second intervals during a 1-minute period for a car…

A: Here the given table shows speedometer readings at 10 second intervals during a 1 minute period

Q: The function C(t)=C0(1+r)^t models the rise in the cost of a product that has a cost of C0 today,…

A: The Present cost of boat is The Average inflation rate is  for 2 yearsTherefore, we have to find the…

Q: Consider the function f(x, y) = X (defined whenever y = 0). Y (a) Find the equations of the level…

A:

Q: Consider the differential equation (2y+32) dz +(2x+3y) dy = Which of the following is true? [Select]…

A: Given,

Q: 1 2 - dx = (y + ¹)² dy X y ln x

A: Given the differential equation :

Q: The function g is related to one of the parent functions described in an earlier section. 9(x) = √3x…

A: The objective of the question is to identify the parent function of g(x), describe the…

Q: 3. Find each of the following limits algebraically (without generating a table of values, graphing…

A:

Q: Use the graph of f and g. Let p(x) = f(x)g(x) and q(x) = f(x)/g(x). Find p'(8)= and q'(5)=

A:

Q: Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter…

A:

Q: Explain the meaning of lim r(x) = L. x→a* As approaches from the values of approach ....

A: Given value of limit is,

Q: 3. If f(x)=5-x² f(x + h) - f(x),x ‡0 h a) Evaluate b) Solve f(x) =0 c) Does f(x) have a Local…

A:

Q: For f(x)=x4, the instantaneous rate of change is known to be 108 at x = 3. Find the equation of the…

A: For f(x) =x4 the instantaneous rate of change is known to be 108 at x= 3.

Q: 9) Enter the exact value (no decimals) of the es Sin (Cos' (²)) =

A: Since you have asked multiple question in single window , as a guideline i can only solve first one…

Q: Revenue The revenue (in dollars) from the sale of a infant car seats is given by R(x) = 70x -0.02x²,…

A: The objective of the question is to find the derivative of the revenue function R(x) = 70x - 0.02x².…

Q: Let f(x) = lim I→7 [7x-1 5 z+4 Show that f(x) has a jump discontinuity at x = 7 by calculating the…

A:

Q: The terms of a series a, are defined recursively. Determine the convergence or divergence of the 22…

A: The term of series are defined recursively.Given,

Q: Consider the following. f(-4)=-7, f(1) = 4 (a) Write the linear function f that has the given…

A:

Q: FA 2. F(x) H Analysis X-intercept (s): y-intercept: domain: range: vertical asy's: horizontal asy.…

A: The given function is

Q: Find the distance along an arc on the surface of the earth that subtends a central angle of 4…

A: The objective is to find the distance along an arc on the surface of the earth

Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation.…

A: The given equation is

Q: Given A= and B=  a) find the vector that extends from A to B. b) find a unit vector in the same…

A: A=&lt;2, 3&gt; and B=&lt;-1, 5&gt;

Q: A rock is dropped off the edge of a cliff and its distance s (in feet) from the of the cliff after t…

A: Distance after t second, S(t)=16t2S=1600

Q: Use spherical coordinates to evaluate JS = E where E lies between spheres x² + y² + z² = 1 and x² +…

A: given integration  where E lies between spheres x² + y²+ z² = 1 and x² + y²+ z² = 4 in the first…

Q: for small values of hℎ we estimate that riserun=f(π+h)−f(π)h≈

A: The objective of the question is to estimate the value of the expression (f(π + h) - f(π)) / h for…

Q: (A) (B) Let f(x) = −5 – x². Find each of the following: - ƒ(5) – ƒ(2) 5-2 = f(2+ h) - f(2) h -7 =

A:

Q: Find the curvature of the plane curve at the point t = 2. K(2) - y = t³

A:

Q: I dentify the level Write Curve of the function h(x, y) your answer in terms of y as a function

A:

Q: Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). What is the period of the…

A: The graph of the function sec(π2x) the graph is

Q: Part 3: Explain a. Differentiate the following function(s) using the chain rule b. Then,…

A: Note:-Since you asked multiple questions, according to  our policy we can answer only first question…