b) y = -2x2

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that L=∫ab1+[f'(x)]2dxTherefore,L=∫011+dd...

Q: If Ax) = x² + 3x – 2 and g(x) = X+2 then g(f(-1)) is equal to 6.

A: The objective of the question is evaluate the value at the given functions of composition.

Q: 00 Σ n2(n2 + 6) n = 1 1. n2(n2+6) =L>0 converges

A:

Q: Approximate the area below the curve y = (x) from x = 1 to x = 3 by using 5 right endpoints rectangl...

A: Given:   Curve y=12x2            y=x22  From x=1 to x=3 Area using 5 right endpoints rectangles:  ∫a...

Q: 1. If y = V6x + 1, then what is Y? dy? %3D dx dy a. 2(6x – 1) 3(6x + 1)7 2(6x + 1) dy С. dx %3D %3D ...

A:

Q: (use Loug division) | 2x'.3x² +Yx+5 +2 2X-3X +Y x +5

A: Given query is to perform long division.

Q: Given the function y=f(x), y' is found to be negative over the interval (4,8), then over this interv...

A:

Q: (a) Ifx + y = 25, find dy/dx. b) Find an equntio

A:

Q: c) Find the inputs that generate a horizontal tangent line. x2 y = X-1

A:

Q: The derivative of the function y=f(x) at the point x=c is characterized as the of the function at x=...

A: We have to tell what is derivative of function y=f(x) at x=c called ...  a. Slope  b. Point of infle...

Q: Find the derivative of x3tan2x 2x sec2x+3x?tan 2x 6x²sec²2x 3x?tan2x+6xsec²2x 2 xtan2x - 3x²sec²2x

A:

Q: > A Moving to the next Question 2 dz Let z = 6e*v find O 12xy e**y O 18xy e**v O 18x*yex*y A Moving ...

A: Find the derivative

Q: 2π ||미 = 4, ||v|| = 16, 0 = 3 %3D %3D %3D

A:

Q: 2ea dx (ет — 1)2 1

A:

Q: 7. An endangered species of fish has a population that is decreasing exponentially (A(t) = Agekt). T...

A:

Q: 52 Solve G(x) for the given domain. G(x) = x 2 + 2 G(2x - 1) = _____. 4 x 2 + 3 4 x 2 - 3 4 x 2 ...

A:

Q: - 3x + y = 6 ax + 2y = 4 In the system of equations above, a is a constant. For which of the followi...

A: Given :-3x+y=6ax+2y=4

Q: Differentiate the function. 1 f(x) = In .4 %3D f'(x) = %3D

A:

Q: Write the first five terms of the sequence with the given nth term. = sinl an a a3 as

A:

Q: Use the Integral Test to determine the convergence or divergence of the series. 00 Σ 3n + 6 n=1

A:

Q: (1) d?y + 2y = 0 y(0) = 3; dy (at x = 0) = 2 dx? dp, dx d2v dy ....

A:

Q: (0) Using xº = x = x° = 0 (0) (0) %3D Find an iterative solution based on efficiency and advantages ...

A: Let's find. 

Q: Let be the function with first derivative g'(x) = Vx3 + x for x > 0. If g(2) = -7, what is the value...

A:

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below

Q: A researcher is nunning a simulation of an upward rocket to study the upward velocity of the rocket ...

A: v = ulnmomo-qt -gtv=upward velocity 680ms                                u=fuel expelling velocity r...

Q: Use the given vectors u and v to find the magnitudes of vectors u − v and −2u. u = 2i + 4j + 7k, v =...

A:

Q: (b) Suppose $2,100 is borrowed and the interest is compounded continuously. If A(E) is the amount du...

A:

Q: Solve the initial-value problem with the initial condition y0 = 0. dy dt = y + 1 y = ‍   Graph the s...

A:

Q: X+3 is x² -9 The y-intercept for the function f(x)= O (0, -3) 0, O (0, 3)

A:

Q: 1. Find the domain of the function: f (x) = log2 Show a sign table. %3D Intervals: Test Value: Sign ...

A:

Q: Find the derivative of the vector function below r(x) = sin²(secx?)i +csc°(Vx² +1] 2 dd fil

A: Given: - The vector function is, r(x)=sin2(secx2) i+csc3x2+1j+8tan(x2) k To find: -The derivative of...

Q: If a and B, are two angles in standard position in Quadrant II, find sin(a - B) for the given fun 5 ...

A:

Q: 1. Find the work done by the force F(x, y, z) = (xz, z² – x, y ), along C, the curve defined by x = ...

A:

Q: Match the sequence with the given nth term with its graph. 10n %3D n + 1 10 2- 8 4. 主十 2 4 6 8 10 -1...

A: topic - sequence and series

Q: u = (5, 5) v = (7, 1) %3D

A: Given : u=&lt;5, 5&gt; v=&lt;7, 1&gt;

Q: What is the equation of the tangent line to the curve y = x2 – 2x + 1 at point (3,4)? a. y = -4x + 8...

A: as per guidelines I can only do first 3 subparts

Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 4 %3D k! k=0 4...

A: Taylor's series about x=x0 for the function ex; x0=4

Q: 2 3n + 4 Use the Integral Test to determine the convergence or divergence of the series. n= 1 Step 1...

A:

Q: Simplify the expression cos2x + cos x + sin2 x + 1

A:

Q: SOLID MENSURATION I 4. A tower 125 feet high stands on the side of a hill. At the point 240 feet fro...

A:

Q: Find dydx? for f(x, y) = eXy

A:

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A:

Q: f(x+h)-f(x) determine the derivative/ slope of tangent for = lim h→0 h -1 2x 5a) Using the formula M...

A:

Q: Use the disk/washer method to set up a definite integral (set up only, do not evaluate the integral)...

A:

Q: Find if converging or diverging using nth term test

A: ∑n=1∞-1nn5    an = -1nn5    We can now proceed with nth term test.. 

Q: 13 The polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0 has solution set _____. {3 + i, 2 - i, 3,...

A:

Q: Suppose f(x, y) = x² + 2æy+ y². Which field plot is Vf? Justify your answer. 鹿

A:

Q: In the quadratic equation Ax2+ Bx + C=0 describe the roots when 32 -4AC is negative. The roots are r...

A:

Q: C. log2(x + 5) = 2 – log2(x + 8) d. 139x = 16r-9 %3D

A: Here student ask only c and d part

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1....

A: