Prove the following using the definition of a limit. n - 1 (a) lim 1 n+on+ 1 (b) lim (2x² − 3) = −3 x-0 1 (c) lim x2-x²-4 = +∞

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, 0, 0),…

A: Given points  P ( 0, 0, 0) and  Q ( 1, 9, 3)

Q: Find dy if y=t² & t = √h and h = x² dx

A: Given :y=t2t=hh=x2

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A:

Q: For what value of Ⓒ is cotⒸ undefined? 1.0⁰ II. 180° III. 270⁰ Olonly OI and III only OI and II only…

A: This question is related to trigonometric ratios, we will solve it using given information.

Q: LT of Heaviside Write the solution for f(t+5)e-stdt. LT of Dirac Evaluate 8(t-5)e-st dt

A:

Q: Assume that z = f(w), w = g(x,y), x=4r³-s², and y = re. If g (4,1)=-4, g,(4,1)=2, f'(7)= -2, and…

A:

Q: Graph the function f(x) = −2log (x+5) -8 on the axes below. You must plot the asymptote and any two…

A:

Q: Which of the following describes the graph of g(x) = -In(x − 4)? *Ty 8 7 6 5 4 2 2 1 -10 6 7 8 -2 -3…

A: We have to choose correct option

Q: For j(x)=3*-¹, find j(x+h)-j(x) h 3x-1(3h) h 3x-1(3-1) h 3x-1(3+1) h ○(x-1)(3+1) h

A: Topic = Functions

Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

A:

Q: A parabola is modeled with the equation x² - 12x + 4y + 24 = 0. Which is the domain and range of the…

A: This question is based on Parabolic function domain and range.

Q: Express e in the form a + ib. (Simplify your answer completely.) z = -0.26-7

A:

Q: Find the inverse function f¯1 of the function f. Find the range of f and the domain and range of f T…

A:

Q: = 2 and The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x…

A:

Q: Let G=7f-g, where the graphs of f and g are shown in the figure to the right. Find the following…

A:

Q: The graph of f(x) is shown below. Which of the following statements are true? y -7 -6 -3 -2 Select…

A: Here we have to choose the correct option.

Q: Find the definite integral of the items below from a=0 and b =1: Show your solution thanks!!

A: Solve the following

Q: Question 12 Which of the following sections cannot be obtained from a cone? Select one: O A.…

A: if we cut the cone horizontally we get circle

Q: Determine the domain and range of the function. 2+ 1 1-3 1-2

A:

Q: 2π sin(30) de 5+cos² (0)

A:

Q: TU The result of f fysinxdxdy = O 1 O -1 O 1.5 O -1.5

A:

Q: Write an equation describing the relationship of the given variables. y varies directly as the…

A: Given, y is directly as the fourth power of x That is, y=kx4

Q: 12. What is the width in kilometers of a single time zone at a latitude of 40 degrees? (Note: At 1…

A: . What is the width in kilometers of a single time zone at a latitude of 40 degrees? (Note: At 1…

Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz

A:

Q: (c) Find the polar coordinates of the point P whose rectangular coordinates are (2,-6).

A:

Q: Core Laplace Which of the following represents the Laplace transform L[g] (s) So g(t)e="tdt…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: following function show that the @f(z)=3z²+57-6 f(2)=4e²+ sinz b are analytic

A: Above question is solved.

Q: y = (x²+4)* Use Logarithmic Differentiation to find dy dx = dy dx

A:

Q: Graph the line with slope passing through the point (1, 3). 4 X 5 ?

A:

Q: Find the equation of a line tangential to the curve y = 2x² + 7x + 9 at P(1,18).

A:

Q: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40…

A:

Q: What is the domain for the exponential function f(x) = -5log(x-2)? OD: (xe R) OD: (xe R|x>-2) OD:…

A: Here we have to find the domain of the given function.

Q: and the local maxima, local minima, and saddle points of the function, f(x, y) = x³ + 3xy + y³

A: Topic = Derivative

Q: 3. Find the limit of the sequence 12n5 6n5 +47 :} or determine that it diverges.

A:

Q: dy Find for y = dx dy dx 1 13

A: The required derivative is given below

Q: Find the general solution of the following equations: a.(d^3y/dx^3)−2(?^2y/dx^2)−3(dy/dx)=0…

A: We need to solve D.E.

Q: 3. fx²4 dx 5. dx 3x² + 1 +x dx u= U= U= du = du = du = answer: answer: answer:

A:

Q: Which of the following is the average rate of change over the interval [-2, 5] for the function g(x)…

A:

Q: S²₁₂ So 1-y² √x² + y² √x²+y² xyzdzdxdy

A: We know that integration power rule is - Integration of xn is xn+1/n+1 +C . Here C is integral…

Q: √9-x²2x √ O O√9-² % √9-2 - - Arcs + C +Arc3in Ễ+ế

A:

Q: Express (+)² in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] 3 [cos 70+isin 701

A:

Q: 1. Find the arc length of the curve f(x) = 3 4 (x + 2)2 on the interval [0, 4]. 3

A: Find the arc length

Q: what is after the negative 4 is that Cos I can't tell what that is supposed to be

A:

Q: 5- Find the volume of the box (parallelepiped) determined by the vectors 0 = (0,0,0), B = (1,1,2)…

A:

Q: x² - 4 S √3x² +18x+27 dx

A:

Q: Use partial fraction decomposition technique to evaluate the integral: x² S dx. (x+1)3

A:

Q: & Q6/(A)Evalute e*² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: In this question we have to find the Integration and partial derivative.

Q: 6. Dustin is trying to design a weapon to fight the Demogorgon. His model has three planes, and he…

A:

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: Area of a circle C. Use definite integration to show that the area enclosed by a circle of radius 1…

A: