Find the first partial derivatives of the given function.

Q: Explain how you would graph the equation y + ∣y∣ = x + ∣x∣. Then sketch the graph

A: Given: y+y=x+x for drawing graph of given function, first we simplify it so, if x<0, y>0 then ...

Q: Explain why each of the following integrals is improper.

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: (a) Use the Generalized Mean Value Theorem to furnish a proof of the 0/0 case of L’Hospital’s Rule

A: L'Hospital;s Rule is applicable only: (i) In case of the ratio of two functions f(x) and g(x). (ii) ...

Q: Evaluate the following integrals.

A: It is given that, ∫sin 2x lnsin x dxWe have to evaluate it.    

Q: Find a positive angle less than 360° that is coterminal with a -135° angle.?

A: Concept - A coterminal angle is calculated by adding and subtracting 360 degrees from the angle give...

Q: I| Fx.y)dxdy, the change of order is For

A:

Q: The rectangular plot of land shown in the figure is to be fenced along three sides using 39 feet of ...

A: Total fencing is 39 feet and the total area of the plot is 180 square feet. That is, x+x+y=39⇒2x+y=3...

Q: (a) Use a graph of              ______________       ______________f(x) = √3 x2 + 8x + 6  -  √3 x2 +...

A: From the graph, the value of  f(x) to one decimal place islimx→∞ 3x2 + 8x + 6 - 3x2 + 3x + 1 ≈ 1.4

Q: Consider the set:List all numbers from the set that are a. natural numbers,b. whole numbers, c. inte...

A: according to given data natural numbers=81whole numbers=0,81integers=-17, 0, 81rational numbers=-17,...

Q: Solve , (D^3+D^2-4D-4)y = 8x+8+6e^(-x)

A: Given: Solve (D3+D2-4D-4)y=8x+8+6e-x

Q: Use properties of logarithms to expand the logarithmic expression logb(x3y/z2) as much as possible. ...

A: Consider the following:Product Rule:logxy=logx+logyQuotient Rule:logxy=logx−logyLog of power:logxy=y...

Q: Determine whether each graph is the graph of an even function, an odd function, or a function that i...

A: if a function is even then the graph is symmetric about the y-axis and if the function is odd then t...

Q: Suppose the functions ƒ(x) and g(x) are defined for all x and thatlimx→0 ƒ(x) = 1/2 and limx→0 g(x) ...

A: Given limx→0fx=12 and limx→0gx=2we have to findfx.cosxx-1

Q: Use the laws of logarithms to evaluate log 2    80 -  log 2   5

A: Given: x=log280-log25 we know that logm-logn=logmn                                                  ...

Q: Find the local extreme values of ƒ(x, y) = x2 + y2 - 4y + 9.

A: Given: fx,y=x2+y2-4y+9

Q: (a). Determine whether the following function f(x) = -5z+6 when a 3 is continuous at x = 3. Justify...

A:

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: ∫lnxx2 dx=∫lnx·x-2 dx=lnx·∫x-2 dx-∫dlnxdx·∫x-2 dx dx=lnx·x-2+1-2+1-∫1x·x-2+1-2+1 dx=-lnxx+∫1x2 dx=-l...

Q: Atmospheric Pressure Atmospheric pressure P (in kilopas- cals, kPa) at altitude h (in kilometers, km...

A: we have been given the formula  lnPP0=-hk where k=7 and P0 = 100kPa are constants and we have to sol...

Q: Find the sums of the series

A: The given infinite series is: We see that,  

Q: Suppose the functions f, g, h, r and l are defined as follows: f (x) logs + log, r g (x) V(x - 3)2 h...

A: As per the bartleby guidelines from more than one part only one has to be solved. Please upload the ...

Q: Evaluate the integrals

A: To evaluate the integral: ∫-11∫01∫02x+y+zdx dy dz Evaluating the integral: ∫-11∫01∫02x+y+zdx dy dz=∫...

Q: Intersection points Find the intersection points of the following curve.

A: Given curves,  r = √3 r = 2 cos 2θ To find the intersection of the curves. 

Q: Fill in the blank/s: The formula for nCr has the same numerator as theformula for nPr but contains a...

A: We have to fill in the blanks: The formula for Crn has the same numerator as the formula for Prn but...

Q: Evaluate x(x2 + 1)3 dx.

A: Given ∫x(x2+1)3dx

Q: Find the derivative of the function. 6. s(t) = 49 (6t - 7) %3D s'(t) =D %3D

A: Use the formula for derivative of a power of a function.

Q: Use the definition of continuity and the properties oflimits to show that the function              ...

A: Consider the given function as fx=x16-x2

Q: If the function f(x) = {cos(2πx−a),x<−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x<-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,...

Q: The relationship between f and g is given. Explain the relationship between     f′ and g′. g(x) = −5...

A: Given relationship between f(x) and g(x) is - g(x) =-5f(x)            ...............(1)Differentiat...

Q: Show that the conjugate of the sum (product, or quotient) of two complex numbers, z1 and z2 , is the...

A: Let z1 = a+ib and z2 = c+id be two complex numbers. Then we get, Conjugate of z1 is = a-ib Conjugate...

Q: (a). If s(t) = +to + t², 0 <t< -2, gives the position of a moving particle at time t, then what time...

A:

Q: Power series for derivativesa. Differentiate the Taylor series centered at 0 for the following funct...

A: Taylor series of function fx at a is defined as:fx=fa+f'a1!x−a+f''a2!x−a2+f'''a3!x−a3+…Consider the ...

Q: Find the gradient of the function w = x tan( y + z), at the given point (4, 3, −1)

A:

Q: 21(a) Evaluate dx by partial fraction method. x+9x²+14x

A: Given:∫5x3+9x2+14xdx

Q: A race Runner A begins at the point s(0) = 0 and runs on a straightand level road with velocity ν(t)...

A: Given: Runner A start at the point s0=0 and run with velocity vt=2t and runner B start at point s0=8...

Q: Is the sum of two rational numbers always a rationalnumber?

A: Given: Let a/b and c/d be two rational numbers where a ,b ,c and d are integers ,b and c not equal t...

Q: The function defined by f(x)= x' -3x² for all real numbers x has a relative maximum at x = Select on...

A: Given function is fx=x3-3x2. Differentiating the given function with respect to x, f'x=3x2-6x For cr...

Q: 4n2 +n (a) Check the convergence of the series E using limit comparison test. n=o n°+6n2 – n (b) For...

A: