Let z(1, y) ry where a = r cos(30) & y = r sin( – 70). az дл ду дл ду az & ae Calculate by first finding & and using the chain rule. ar ar ar' ae ae Note: To produce the 0 symbol, type the word "theta". az Preview ar az Preview || ||

Q: b. Let g(x) = x² – 7. Determine the root(s) of g. 7,-7 Preview 7 = 7., – 7 = -7. c. Let h(x) 5x? - 3...

A: Topic = Algebra

Q: Question 8 ... (sin x – 1) dx + | (cos x + 1) dx = 4 C.) – 1 D.) - (1+) А.) —89 В.) —91 2 A A в) в D

A:

Q: Linear differential equation hith constart coefficients. 3 D = n- 4R+ 6) y

A: Given: D4-4D3+7D2-4D+6y=0

Q: 6x³ – 1 у — 2х + 1 3x* - 4

A:

Q: A function f is said to have a removable discontinuity at a if: is either not defined or not continu...

A:

Q: Linear differential equetion with constand coefficients -メ ダーンツ e

A:

Q: 15 4 -4-3 -2 4 2- -3 3.

A: Accordimg to given graph a. As x→-2-  fx→∞b. As x→-2+  fx→-∞

Q: Let f(æ) = sin(x) and g(æ) = x² . Find (go f)'(x) O 2sin(x)cos(x) O 2xcos(x?) -2æcos(x?) 2xcos(x)

A: Given that f(x)= sinx and g(x)=x2. And we find (g0f)'(x). We know that d(xn)/dx = nxn-1.     Here i ...

Q: Find the slope of the curve at the indicated point. find the equations of the tangent and normal lin...

A: Follow the procedure given below.

Q: Question 16 dx What should be the rewrite of the integrand of S so that the resulting integral is in...

A:

Q: For the following initial value problem, find the general solution, express the arbitrary constant C...

A:

Q: (b) Given the first-order differential equation as below: (x² +3y² +5)dx+(6xy +6y+3)dy = 0 (i) Ident...

A:

Q: What should be the rewrite of the integrand of dx so that the resulting integral is integrable?. 4+2...

A:

Q: A population of bacteria has 1175 bacteria in its starting population. The half-ife of this particul...

A: Given:   Bacteria : 1175     Days : 14

Q: 15. A particle moves along a straight line and has acceleration given by s"(t) = 5t + 3. Its initial...

A:

Q: Explain what it means to say that: lim, h(x) - o and lim h(x) x →5+ – 0.7. x →4 As x approaches 5 th...

A: According to question,Given limits,limx→4 hx = -∞,andlimx→5+ hx = -0.7,

Q: To evaluate f dx, the integrand can be transformed to 1-sin?x

A: Follow the procedure given below

Q: Question 12 dy If dx and y = when x = 1, find y(2). %3D V3x-2 2 (A) 27 40 B) 27 27 26 27

A:

Q: Using incremental search with x1 = 1.5 and Ax = 0.01, %3D %3D approximate the solution of Inx = = 2-...

A: fx=lnx - 2+xx1=1.5∆x=0.01tolerance=0.05----------------Find: To find 'x=a' such that fa = 0±0.05.  -...

Q: uity?

A: We will find the functional value at x=2.

Q: Use the graph to answer the question. Is f continuous at x = 0? %3D -4- -5- 2.

A:

Q: Evaluate the given limits numerically and graphically: lim /x² – 36 X-6 1. 4. X-3 x2 - 9 1 lim 2 Vx2...

A: 2. The given limit is limx→21x2-4.   It is evaluated as follows: If limx→a-fx≠limx→a+fx then the lim...

Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin ...

A:

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(a + h) – f(a) f(x) ...

A: We have to use the given formula to calculate the difference quotient

Q: * Limits of Polynomial, Rational, & Radical Functions Evaluate the given limits. 1. lim Vx+ 16 X-7

A: Here we have to evaluate the given limit.

Q: Breble Find the volume of the solid whose base is the region inside the unit circle x2 + y? = 1, and...

A: We need to find volume.

Q: In Problems 63-68, find f' (x) and find the value(s) of x where the tangent line is horizontal. 65. ...

A:

Q: The table below shows the cost, C, of selling x cups of coffee per day from a cart. Determine if the...

A:

Q: Sketch a possible graph of a function that satisfies the given conditions. f(-1) = -7; lim f(x) = -2...

A: Given that f(-1) = -7. Therefore (-1,7) is a point on the graph .when x tends to -1 from the left si...

Q: Q2 Second-order non-homogeneous ordinary differential equation given as; y" + 3y' –10y = e2x Calcula...

A:

Q: The Laplace Transform of

A:

Q: Determine the behavior of the functions defined below. Note that it is common to write g(x) → 0" to ...

A:

Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocity i...

A:

Q: dx What should be the rewrite of the integrand of f so that the resulting integral is integrable? 1+...

A: We have to find integrand 

Q: 15. A particle moves along a straight line and has acceleration given by s"(t) = 5t + 3. Its initial...

A:

Q: 15. A particle moves along a straight line and has acceleration given by s"(t) = 5t + 3. Its initial...

A:

Q: In Problems 67-72, use the demand equation to find the revenue function. Sketch the graph of the rev...

A:

Q: If dx dy and y = 27 14 when x = 1, find y(2). %3D 3x-2

A: ∫x3x-2dx

Q: Solve the differential equation y' = e4Y sin(5x) and choose the correct answer from the following op...

A: Given:- y'=e4y sin(5x)  To find:- General solution of given differential equation

Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y = 2x– y d...

A:

Q: Find the center of mass of a thin plate of covering the region between the x-axis and the curve y = ...

A:

Q: If f(x) = Vr, match each formula to its corresponding graph. the graph in red 1. g(x) = -f(2x) 2. h(...

A:

Q: 17. A boat is being pulled toward a dock as shown in the figure. If the rope is being pulled in at 3...

A: Follow the procedure given below. 

Q: What should be the rewrite of the integrand of f dx so that the resulting integral is integrable? x2...

A: solution:-∫2x+52x2dxnow,2x+52x2=4x2+20x+25x2              =4x2x2+20xx2+25x2              =4+20x-1+25...

Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = 2x2 + 3xy...

A:

Q: road length (in kilometers), T is the total county land area (in hundred-acres (Ha)), U is the urban...

A: We will find the number of accidents. 

Q: A. Manually Sketch the curve with the given polar equation by first sketching the graph of as a func...

A: Given:         r=cos5θ

Q: The slope of a curve is given as (2x + b and has a value of at 16 2x3 x = 2. What is the value of y ...

A: Given slope of curve dydx=2x+b+12x3

Q: Let X be the set {5, –6, 2}. For the first three parts of this problem you are asked to define a fun...

A: Consider the set 5,-6,2. The function is f:X→X and the relation is u~w⇔w=fu.   a) The relation is re...

Q: Evaluate the integral fw(2w +3)² dw A.) w+4w3+w² + C B.) w+2w3+9w² + C C.) w2(w²+4w+9/2) + C D.) 2w ...

A: