Assume that ƒ(x) is everywhere continuous and it is given to you that ƒ(2) = −7 and f(x)+7 lim x→2 x-2 = 8. It follows that y= is the equation of the tangent line to y = f(x) at the point ( Number " Number ).

Q: Suppose Use this to compute the following limit. Limit= Number What Theorem did you use to arrive at…

A: Snadwich TheoremSqueeze Theorem:  If g(x)≤f(x)≤h(x)  for all x in an interval containing a point…

Q: A car has 12,500 miles on its odometer. Say the car is driven anaverage of 40 miles per day. Choose…

A: Given data:- A car has 12500 miles on its odometer Car is driven an average of 40 miles per day N is…

Q: Which of the equations below is a second order nonlinear differential equation? A. 2 x²y - (1 - dx)²…

A: To find the nonlinear equations.

Q: Find dx dx || by implicit differentiation. 6x² + 7xy - y² = 8

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

A: By using synthetic division method the solution of given problem is as follow

Q: Find a general formula for f(n). ƒ(x) = (x + 7)−¹

A:

Q: 2. Use the graph below to determine whether the statements about the function y = f(x) are true or…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, the…

Q: Consider the function f(x) = 3x²-5x+2. Use it to find f(4), f(-1), and f(a + 3). f(4) = 30 O…

A:

Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: A coroner arrives at a murder scene at 7 p.m. She finds the temperature of the body to be 84 3°F.…

A:

Q: Geometry A wire of length x is bent into the shape of asquare.(a) Express the perimeter p of the…

A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

Q: Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the…

A: Concept used: Graphing A graph of a function is a line that represents the function on a coordinate…

Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows

Q: Determine whether or not the following equation is exact: 3 dy xy + (²x² + 2y² − 20) = 0, y(0)=1. dx…

A: See this solution in below

Q: dy What is the IF for solving the linear equation: x dx O O O O A. 3 X2 B. 3x 2 C. 3 -Lnx D. E. 3x e…

A: It is linear differential equation

Q: 4. Find the limit. lim x-0 lim X-0 5+5x+ sin x 6 cos x 5+ 5x + sin x 6 cos x CA. Yes, lim f(x)…

A:

Q: Evaluate the limit lim x →∞ 5x² + 3x 7x4 + 2x² + 10

A:

Q: Integrate [8³e³ 13 ft³e est dt t³ est dt. =

A: The solution to find the integral  of given integration is as follow.

Q: Uranium-238 (U-238) has a half-life of 4.5 billion years Geologists find a rock containing a mixture…

A: Half life = 4.5 billion years N(t)=0.77* N0t= ?t12=4.5 billion years

Q: If the endpoints of a diameter of a circle are 14, - 52 and 1 - 6, 32, find the center and radius of…

A: Given: The endpoints of a diameter of a circle are (4,-5) and (-6,3). To find: The center and radius…

Q: Problems: 1.(x³ + xy² − y)dx + (y³ + x²y + x)dy = 0 2. (ex siny + ey)dx - (xe-y-e* cosy)dy = 0

A:

Q: Find the following limit. lim x-x 2+ x - 4x³-4 5 x³x²+1 Number

A: ans=  -4/5

Q: Given the matrix find A. Write A as input your answer below: a1 = 012 021= 022= H EI I EE A³ - [:…

A: The matrix is given by A = 220-3 To evaluate: The value of A3

Q: Uranium-238 (0-23 has a hall-me of 4. and determine that 67% of the original U-238 remains; the…

A: We will find the age of rock.

Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy dx…

A:

Q: Prove that every Cauchy sequence is bounded. Attach File

A:

Q: (d) below. OA. OA. Let f(x)= O A. a. Find lim f(x). Select the correct choice below and, if…

A:

Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y − 2z subject…

A: Given function fx,y,z=2x+y-2z Let gx,y,z=x2+y2+z-2025

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

A:

Q: Evaluate the following integral. dt -1² +8t-15 Rewrite the integrand by completing the square in the…

A: First of all we will solve the denominator then we will solve the integration.

Q: dy What is the IF for solving the linear equation: x + = C0SX,x >0 dx 2 O O O O A. B. D. E. MIN 3x 2…

A: To find IF

Q: dP Which among the choices is the same as the differential equation = P(C₁ - C₂P)? dt A. OB. dP dt…

A:

Q: 11. For the following series, is it convergent? If yes, is it absolutely convergent? Σ+1 1 n=1 Α

A: See this solution in below.

Q: Calculate the slope of the line that passes through (-11, -6) and (1, -4). O - 1 O -16 1 O 6

A:

Q: A (B) f(x) is continuous at.x=3 D lim f (x) exists x-3 (C) f(3) exists Based on the graph above,…

A:

Q: 2. y=x+c₁e* + C₂е¯x

A: Given :y=x+c1ex+c2e-x

Q: If the rational function y = r(x) has the horizontal asymptote y = 8, then y → Need Help? Read It as…

A:

Q: 1 If (-x) = -5 ON) - M O O A. e5 B. ن D. E. y5 y -5 then what is the integrating factor? None of the…

A: Given: ∂M∂y-∂N∂x1M=-5y To find: Integrating factor.

Q: f(x)= (ln x)^3 f'(x)=

A: Given, f(x)= (ln x)^3

Q: 3. Elimination of Arbitrary Contants 1. y = peax cosbx + peax sin bx 2. y = C₁x + c₂ex ; a and b are…

A: Here we have to eliminate the arbitrary constants of the equation y=ϕeaxcosbx+ψeaxsinbx…

Q: Which of the following statement is TRUE? O A. An ordinary differential equation (ODE) contains…

A:

Q: (d) Let y(x) = [tan-¹ (√)]4. Find y'.

A:

Q: Find the general solution of the differential equation y" + (wo)²y = cos(wt), w² ‡ (wo)². NOTE: Use…

A: Solution: Given data, y"+(w0)2y=cos(wt) Lets compose the auxiliary equation m2 + w02  =0 m1 = iw0 m2…

Q: Evaluate the difference quotient for f(x) = −x³ +· O 3x²+3xh-h² O h² O-h² O-3x²-3xh-h²

A: See the details solution in below

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A:

Q: The answer was not correct... i think they were wanting some kind of answer closer to like…

A:

Q: You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and…

A: Given data:- The given angle is, θ=80° The given diameter is, d=12 in So, the radius is, r=6 in.

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A:

Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Condition for existence of limit at x=a⇒limx→a-fx=⇒limx→a+fx=⇒limx→afx

Q: Eliminate the arbitrary constants of y=ce*+₂4-sin3x

A: