Use long division to divide. (x³+ 4x²+x+ 4)÷ (x+ 4) x²+ 8x+ 33 x2+ 1 120 x²+ 8x+ 33+ x+ 4 x²– 4 129 x²+ 8x+ 33-- x+ 4

Q: Radioactive elements disintegrate spontaneously in a process called radioactive decay. The rate of…

A:

Q: Each side of a square is increasing at a rate of 3 cm / s . At what rate (in cm^ 2 /s) is the area…

A:

Q: Find the first partial derivatives of the function. x9 - y5 f(x, y) = x + y fy =

A: The objective is to find the partial derivatives of the function.

Q: Evaluate the definite integral. 13 i+ej+t k dt O e13 – 1 -(61 -1) + 1 13 e13 i- (e- - 1) j+ 1 13 2…

A: We have to find the integral

Q: A theorem states that one local extremum implies absolute extremum. Verify that the following…

A: A(r)=12r+3πr2 , r>0SupposeA'(r)=0(-1r2×12)+6πr=0-12+6πr3=0 ⇒r3=126π⇒r3=2π⇒r=2π3

Q: dx J (x² + 2x – 10)²

A:

Q: Suppose a tour guide has a bus that holds a maximum of 100 people. Assume his profit (in dollars)…

A: P(n) = n(50 - 0.5n) - 100 P(n) = 50n - 0.5n2 - 100 Domain : [ 0,100 ] Now, P'(n) = 50 - n  To Find…

Q: Follow the format of solution of the picture below and show checking.  348610 B2 B8 B16

A:

Q: Evaluate the limit. Leave results in exact form. V9 + 7r2 lim 11 + 3x

A: This question is based on limits of inf/inf form.

Q: Find the area enclosed by the given parametric curve and the x-axis. x = 2 sin(t),  y = sin(t)…

A:

Q: Evaluate the following limits. If needed, enter INF for o and MINF for -0. (a) It – 9 lim t²+5t +5…

A:

Q: cot'x csc'xdx 4.

A:

Q: INTEGRATION OF TRIGONOMETRIC FUNCTIONS AND ITS TRANSFORMATIONS Evaluate the given integrals. Please…

A: Evaluate the integral :   ∫5cosxcot2sinxdx

Q: Select the answer option that corresponds with polar coordinates (1, -). 90° W/2 150° 45 1 7 radians…

A:

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?…

A:

Q: x =r' +1, y=r -t d'y d’y b) Find dx?

A: Given: x=t3+1 and y=t2-1

Q: Evaluate the first derivative of the following functions: g(x) : = cosx – sinx f (x) = 4x²cosx g(y)…

A:

Q: Use the formula k(t) = r(t) × r"(t)|| ||r(t)||° to find k(t). r(t) = 7 cos(8t)i+7 sin(8t)j + tk K(t)…

A:

Q: 1.82 Let E CR be any unbounded set. Find an open cover of E that has no finite subcover. Prove that…

A: We will proceed as follows

Q: 14.A girl walks 2 km due east from a fixed point O to A, and then 3 km due south from A to B. Find…

A:

Q: 4x 20. Write log2 assthe sum and/or difference of ² - 3x - 18 logarithms. Express powers as factors.

A: The given logarthim expression,       log24x3x2-3x-18

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

A:

Q: Given the function: if x 1 Find A given that f is continuous at x 1. f(x) = %3D

A:

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A:

Q: Cases and Complements 1. A group of four animals will be selected for adoption from a group of 10…

A:

Q: Consider the following. u = x w = Vx y = xx Calculate the following. Simplify your answers. du dx dw…

A:

Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

A:

Q: Let f''(x) = 36 sin(6x) and suppose f'(0) 6 and f(0) = 4. Find f(5) a(;) =

A:

Q: What is the integral of x" cos ax dx ? хN sin ax А. -=S nx"-1 sin ax dx + а а хN sin ax B. n -"Sxn-1…

A:

Q: Find real numbers a and b such that the equation is true. a + bi = 2+6i a = 3,6 = 2 a = 5,6 = 9 a =…

A: To find the values of a and b.

Q: 4. Calculate the area of the bounded region x= y+3 y=3 x= 1 1112 A. 52/3 (. 32/3 B. 8/3 D. 15/3

A:

Q: 2y +1 e'y 1+ y? dy dy = t*y dy 4. dt 2. 3. %3D dt dt t

A: See the answer below

Q: Write the quotient in standard form. 11 1-i

A: Topic = Complex number

Q: Perform the operation and write the result in standard form. 3 4 1+i 1-i 7. +

A:

Q: INTEGRATION OF TRIGONOMETRIC FUNCTIONS AND ITS TRANSFORMATIONS Evaluate the given integrals. Please…

A:

Q: b. g = f(t, v) = tv, t = In m v = m %3|

A: Given g=tv, t=ln(m) and v=m6

Q: Find the amplitude and period of the function. y = 3 + 1/2 cos(?x) amplitude=           period=…

A:

Q: The absolute maximum and absolute minimum value of the function f(x) = 3x – in [-1,4] %3D is: 4.5, 4…

A:

Q: If f(x, y) = 7xey + 7y Inx, then is given by: дудх O 49e5y + 7/x 35eby + 7/x O 25e5y + 7/x O 35e5y +…

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: The domain of a vector function is the intersection of domain of its components.

Q: Find the amplitude, period, and phase shift of y = 4 cos (2x). (Express numbers in exact form. Use…

A:

Q: Use Mean-Value theorem to find c X +2x-1 ; [o,i] xj[3,5] Use L'Hôspital vule to find the wmit lime…

A: We will solve the Problem on limits and mean value theorem.

Q: 4. Determine the general equation of the plane containing the points P(1, –4, –5), 3 Q(2,0, 13) and…

A:

Q: Choose the point which shows the correct location for the polar coordinate (-3, 315). 90 2 WIN 135…

A: The given polar coordinate -3, 315°

Q: 5* Determine whether the sequence defined by a* %3D 8* +1 converges or diverges. If it converges,…

A:

Q: Determine whether Rolle's Theorem applies to the following function on the given interval. If so,…

A: rolls theorem

Q: b. g = f(t, v) = tv, t = In m v = m

A: We can solve this as follows:

Q: Approximate the area under the graph of f(x) 1 over the interval (0, 4] using five rectangles. x +1…

A: Let's find.

Q: Use the graphing utility to plot the graphs of y = cos (x) and y = 2x. (Enter multiple functions of…

A: We will graph the functions.

Q: Consider the function below. f(t) = t + cost, -2n sts 2n (a) Find the interval of increase. (Enter…

A: