A. Use the definition of derivatives to determine the derivatives of the following functions. 1. f(x) = x 2. f(x) = -4x3 – 2 3. f(x) = 1/x 4. f(x) = 1/ (x+1) 5. f(x) = (x+1)/ (x-1)

Q: 2. 52 Calculate the determinant for 2 3

A: As we know that, If the given matrix is A=abcdefghi then the determinant of the matrix is:…

Q: Consider the following lines: 4:z=1,y-1=-4,2=1-3t :z=2s+1,y=1-3s,z=1 y+1 z-1 2a Find the…

A: Explanation of the answer is as follows

Q: Find the general solution of the given system. 10 -5 X' = 8 -12 X(t)

A:

Q: Evaluate the line integral Ĥ. dř where Ĥ = e" î + [xe" + In(2)] ĵ + º Â and the curve C is defined…

A: Given problem:-

Q: Suppose that P dollars in principal is invested for t years at the given interest rates with…

A:

Q: If a student is chosen at random, what is the probability that: Write your answers in percent form.…

A: We have to find the probability.

Q: A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9.8…

A: It is given that a projectile is shot from a cannon, the muzzle velocity is v0=500 m/sec at which…

Q: Find parametric equations for the line whose vector equation is given (a) (x, y) = (3, –5) + t(1,…

A: A)x, y =3, -5 + t 1, -2x, y =3, -5 + t, -2tx, y =3+t, -5-2t Parametric equations of the line:x= 3 +…

Q: Example Find the exact area of the surface obtained by rotating the curve y? = x + 1, 0 <x< 3, about…

A:

Q: Question For the functionf(x) given below, evaluate lim f(xr) and lim f(x). X00 X--00 V3x + 1 -3x -…

A:

Q: 2. f(x) = 9x2 - 1 at x = 1

A:

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: Given t2 - 25 dt 1+ cos2(t) f(r) 0. At what value of I does the local max of f(x) occur? H.

A:

Q: Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function,…

A: The objective is to obtain the maclaurin series of the given function.

Q: Let S be the solid bounded by the planes z = o and y + z = 3, and the cylinder x2+y2 =2y-

A: answer is in next step

Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.

Q: Find an equation of the tangent plane to the surface 3x? + 2xy – 4z2 + 2x – 3y = 0 at the point P(0,…

A:

Q: (-1)" Given: In(1 + x) = if x < 1. n + 1 n=0 (-1)" (n +2) Σ 4. Compute the exact value of 2n+1(n +…

A:

Q: Find the equation of an ellipse satisfying the given conditions Foci: (- 2, 0) and (2, 0); length of…

A: Equation of the ellipse :    x-h2a2+y-k2b2=1 , where (h,k) is the center of the ellipse .Length of…

Q: Find the remaining trigonometric ratios. Зл T < x < 2 1 cos(x) %3D sin(x) tan(x) %3D %3D cot(x)…

A:

Q: Evaluate the surface integral f(r, y, z)dS,

A: answer is in next step

Q: Given: In(1+x) = n+1 if x < 1. n + 1 n=0 2. Evaluate f(2022) (0).

A: To solve the following problem

Q: Find all values of x in the interval [0, 27] that satisfy the equation. (Enter your answers as a…

A:

Q: > (-1)" x3n+2 find the exact value of 5-1)"(3n + 2) By differentiating the power series 8n n=0 n=0

A:

Q: A mdc.blackboard.com B Content Question Completion Status: 10 20 3D 4 50 7 10 11 120 130 14 Find the…

A:

Q: A fish tank initially contains 40 liters of pure water. Brine of constant, but unknown,…

A:

Q: Find the area of the following triangle, OA= 40 OA=80/3 O A= 80 O A= 40/3 RI TH

A:

Q: Under a change of variables æ = u², y= v³ , the infinitesimal element of area dædy becomes 3u?u°dudv…

A:

Q: Part I х2-9 1. lim х>з х-3 х2+5х-6 2. lim X→1 х2—1

A:

Q: Calculate -2 + lỉ. Give your answer in a + bi form. In polar form, use the angle 0 <0 < 2n. a - b -

A:

Q: Consider the following lines 4:z=1,y-1=-4,2=1-3t :z=28+1,y=1-3s,2=1 -y+1 %3D z-1 3a 2a 3 Find the…

A: Explanation of the answer is as follows

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

A: Given equations which bound the region are: x = 8y ; y = 4 ; y = 5 and x =0 The volume of revolution…

Q: 8. f(x) = (6x² + 7x)* 9. f(t) = (4t² + 3t + 2)-2 10. f(x) = (5x* – 7x)2/3

A:

Q: If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and x/2, evaluate the expression using…

A:

Q: Find the point where the function f(x,y, z) = x + 2y + 3z subject to the I takes on its minimum…

A: The given function is f(x,y,z)=x+2y+3z.

Q: n(n + 1)(2n + 1) 3. Le n be a positive integer. Use induction to prove || 6 j=1

A:

Q: n=1 Vn+1 yn +2 Determine if the series converges or diverges. If the series converges, find its sum.…

A:

Q: Question 2r 2x Find the absolute maximum and absolute minimum of the function f(x) = 5 6 over the…

A:

Q: dy Find . da Given: 3x?y + xy = sin (x + y). %3D dy %3D da 2 sin(z+y) cos(r+y)+3ry-ry 2ay? +3ry+2…

A:

Q: Solve the system by using the inverse of the coefficient matrix. X+y+z =1 3x + 4y – z =1 2x - y-z =3…

A: Let A be the coefficient matrix of the system.So,A=11134-12-1-1AX=BX=A-1Bwhere X=xyz, B=113

Q: Oil from a leaking oil tanker radiates outward in the form of a circular film on the surface of the…

A:

Q: Given y = Vx – 2/x – 2; Find y'. O (E) None of the choices Vz-2-1 y = 2/(z-2)(x–2/z-2) VI-2–1 2(x-2)…

A: Given: y=x-2x-2   We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x

Q: Write an equation for the parabola with a vertex at the origin and directrix y = - 24 An equation…

A:

Q: Perform the indicated multiplication if possible. (Enter NONE in any unused answer blanks. If the…

A:

Q: Question 6 Differentiate: arcsin () + arccos (2) = 1 + arccos () = 1 %3D O y/x O (E) None of these O…

A: Derivative dydx of sin-1xy+cos-1yx=1

Q: OQUESTION 14 Find the area enclosed by the given curves. y = 4 - x 2, y = x +2,x= - 2 and x = 2 O…

A: Given query is to find the area enclosed.

Q: Find the graph of the following ellipse. Identify the domain, range, center, vertices, endpoints of…

A: Given:      x225+y216=1

Q: answer

A:

Q: What is the slope of the line 0 = T? (Use decimal notation. Give your answer to three decimal…

A:

Q: 3. -1 1 2 3 4 5 6 7 +1

A: To approximate the area under the curve graphed below from x=2 to x=5 using a Left Endpoint…