Find the limit as →∞ and →∞. Use this information, together with intercepts, to give a rough of the graph. y = x²(x + 2)²(x - 1)

Q: Find an equation of the sphere that passes through the point (3, 1, -3) and has center (1, 6, 5).

A: We use Distance formula between points x1,y1,z1 and x2,y2,z2⇒d=x2-x12+y2-y12+z2-z12

Q: Derive the following functions 2-3x 5 50. y=- 6 3+x 52. y=: 54. y=- Sx²

A: 50. y=2-3x5

Q: 1. Find the general solution: y"

A:

Q: A certain bacteria culture is known to grown at a rate proportional to the number of bacteria…

A: Let Persent number of bacteria =x Rate of grown number of bacteria=dxdt

Q: K Find lim h-0 f(x+h)-f(x) h f(x) = -8x-7, x=2 The lim f(x+h)-f(x) h for the given function and…

A:

Q: a. Use implicit differentiation to find the derivative p. Find the slope of the curve at the given…

A: Given

Q: 2. Determine dy/dx of the following equation. y = a. C. eeez dy dx = dy dx eeez = e. None of the…

A:

Q: Evaluate the indefinite integral S -10x² √1 1-x dx

A: To evaluate the integral

Q: 1 y = f(x) EV 5 4 3 لیا 2- 1 y 0 1 2 lim z 6 lim z 3+ f(x) = f(x) = 3 Enter each answer as a whole…

A: Need to find out the following limits.

Q: x² - 6x - 7 x-7 Fill in the following table. Enter your answers rounded to 3 decimal places. | Y Let…

A:

Q: Find the area of the shaded region. 4 3 2 f(x)=x- 8x +21x, g(x)= -14x + 136

A: We can find the area of the shaded region using the required formula in the below steps.

Q: Compare the right hand and left hand derivatives to determine whether or not the function is…

A:

Q: For an experiment at the University of Montana, Christopher sends an object down a tube 0.4 meters…

A:

Q: 1 c) [xln (25) dx =

A:

Q: 2. Find dx/dy if y = √√1+√x 1 -4√√1+√x Option 3 1 4√√√1+√ Option 1 4√x√√1+√x Option 4 -4√√√1+√x…

A: Solve for the dx/dy

Q: The graph below is the function f(x) -5-4-3-2 Find lim z 2 19 NA Find f(2) Z -2 -3 4 f(x) Find lim…

A: Here we have to use the graph to find the limit of the function.

Q: Find ||7e – 4f||, assuming that e and f are unit vectors such that ||e + f|| = √√. (Give an exact…

A: We have given that....... e=1, f=1 Since,           e+f=32 ,  we have                32= (e+f).(e+f)…

Q: If the demand function for math self-help videos is given by 650.7x, and the total cost function to…

A: If the demand function for math self‐help videos is given by 65-0.7x, and the total cost function to…

Q: 3.) dr de + rcot (0) = r¹ sin(0)

A:

Q: Question 6 Given: y = (16+¹) Z -61² (16+74) 3 √16+t¹ 23 (16+) O (E) None of the choices -21² (16+¹)…

A: Solve for the dy/dt

Q: Solve the problem. For some reason the quality of production decreases as the year progresses at a…

A:

Q: 2. Evaluate the following limit (tabulate). 4- x² lim x→² 3 − √√√x² + 5 O It does not exist O -1 O…

A: Solve the limit

Q: Obtain the differential equation for each family of curves. Identif the complete classification of…

A:

Q: Find the limit. lim X-0 lim X-0 2+5x+ sin x 3 cos x 2+5x+ sin x 3 cos x (Type an integer or a…

A: To calculate limit put the value value of x and simply calculate it Please see the solution in next…

Q: B. 3y² + 2xy = 8 dy dx m TL Equation of tangent line m. NL Equation of normal line

A: Given equation of curve:- 3y2+2xy=8

Q: Using the four-step procedure in finding the derivative of O O -6 (√2x+2Ax+1)(√2+1)…

A: Topic = Derivative

Q: This question is to emphasize how our differentiation rules can be used even when it doesn't look…

A:

Q: Given limx→4f(x)=4limx→4f(x)=4 and limx→4g(x)=4limx→4g(x)=4, Evaluate :  limx→4f(x)+g(x)8f(x). The…

A: See this solution in below.

Q: c) h(t): 5t e (t² + 1)^

A:

Q: lim sec(x) + 7 (x, y) → (0, π/4) 4x - tan(y) sin (1) + 7 4 tan (4) X

A:

Q: Find the G.S. (y2-2xy + 6x) dx - (x2 - 2xy +2) dy=0

A:

Q: Set up and evaluate the definite integral required to find the area of the region between the graph…

A:

Q: Evaluate fi f(x) dx if f(x) = 06 O 12 O 14 08 (2x x-1 if x ≤ 3 if x > 3

A: We need to choose correct option.

Q: (a) Evaluate (5) ex 1+e2x dx

A:

Q: дz дz Let z = sinh(7x + 8y). Find and ax ду дz ax дz ду || 7 cos(7x + 8y) 8 cos(7x + 8y) х х

A:

Q: For an experiment at the University of Maine, Alonso sends an object down a tube 0.2 meters in…

A: Work done  W=∫00.2Fdx Given F=4cosπx4

Q: Determine f-¹(x). ƒ¯¹(x) = = -x² + 16x What is the domain of ƒ-¹(x)? What is the range of ƒ−¹(x)?||…

A: P

Q: omplete the computation. 5, 7, 9) − (7i + 7j) = = |,

A: Given query is to subtract the vectors.

Q: D Question 5 Find dy/dx, given the following: y = | L y P (x²+2x)² 3 (3x²+2) (2³+2x)² + = V (2x-4) 2…

A:

Q: 0.016t The population of a town is increasing at a rate given by P'(t) = 34 e where P is the…

A:

Q: Find the decomposition a = a + a₁ with respect to b if a = (3,4,2), b = (3, 4, 6). ab = (a||x, a|ly,…

A:

Q: Consider the function Compute fx(1, 2) and f,(1, 2) f(x, y) = 3x²y + 5x²y²

A: Given, f(x,y)=3x2y4+5x2y2

Q: 12 лухари у-х2-2х-я сил не 2x-9 and the tangent to the wave curve at the point whose X- coordinate…

A:

Q: The differential equation (x²-y²) y'= 2xy is not an Exact D.E because the partial derivatives of…

A:

Q: Find the areas between curves. Question 1: There are two functions: (1) x = y³ (2) x = y² The…

A:

Q: =t³ - t 24t+1. (a) Where is the particl and at what velocity is it moving when t = 1? (b) When will…

A:

Q: Use vector notation to describe the points that lie in the given configuration. (Let t be an element…

A:

Q: For this discussion post, I will ask you to sketch some graphs that meet a limit condition and…

A: To be found - Sketch of different functions with given conditions. Topic - Function, limits &…

Q: Find the area of the region enclosed by the curves y=x²-7 and y = 9. The area of the region enclosed…

A: This question can be solved using the concept of area between two curves.

Q: Find the equation of the tangent line to the graph of f (x) = 6x2 - 4x + 1, at x=1.

A: