Convert to an equation in rectangular coordinates. r = cos (0) – sin (0) (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Q: (b) Find the direction e of the vector u = .(angle between the positive x-axis and the vector)

A: Topic = vector

Q: Evaluate the integral. (Re du |u3- u?

A: Solution is written in below steps.

Q: For the given functions, find the domain, range and sketch the graph: 1. y = (2 + 3x)/(x – 1) ------...

A: We have to find domain,range and graph

Q: Convert the equation   f(t)=234(0.92)^t to the form  f(t)=ae^kt

A: This question can be solved using the properties of natural logarithm.

Q: Graph the function and find its average value over the given interval. a. g(x) = -|x| on [-1,0] b. f...

A: The objective is to graph the functions and find its average value over the given interval.

Q: QUESTION 10o Select each convergent series from the options below. No work required. 1 n=1 5 n=1

A: P-Test: The series ∑n=1∞1np converges if p>1 and diverges if p≤1 The series ∑n=1∞rn converges if ...

Q: 1. Determine if g is differentiable at r 0 if 2 cos r, if -1<r <0 9(r) = if r20. r+cos r

A:  

Q: 1.)D, show why

A: Answer :- CAN'T TELL. 

Q: Solve for the Linear Differential Equation: y' + y = 1

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Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of ...

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Q: 4x2 – 21x (x - 3)2(2x + 3)

A:

Q: Solve S using the technique of integration by partial x²-4 fractions A. In B. In +c с. in +c D. A В ...

A: Option A 

Q: sin x dx

A: This is a problem of integration. Based on the general formula of integration we will solve the ques...

Q: Evaluate fx²e¬*dx A. -x2e-x – 2xe-x – 2e-x+c B. x²e-x – 2xe=x – 2e-X+C с.-х?е-х — хе-х- 2е-х+с D. x²...

A: ∫x2e-x dxBy using integration by parts=x2∫e-xdx -∫2x∫e-xdx=-x2e-x+2∫xe-xdx

Q: Use Newton-Raphson Method to find the root of x2 + 7x – 10 = 0 with four-digit accuracy . How many f...

A: This is a problem related to numerical method. We will general formula for the method and solve the ...

Q: Find the maximum and minimum values of the function f(x) = In(x) on the interval [1,6] by comparing ...

A: The given function is: f(x)=ln xx

Q: For the given cost function C(x)=40000+700x+x2C(x)=40000+700x+x2, First, find the average cost func...

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Mini...

A: This is a problem of maxima and minima. Based on the general formula we will find out the value.

Q: -3m c2n n S " S" (sin x + cos y)e? dx dy dz A. 2n(e2" + e3") B. 2n(e2". c. 2n(e3 + e2") D. 2n(e – e2...

A:

Q: 9. Sketch the solid obtained by rotating the region underneath the graph of the function f(x) = Vx2 ...

A: The answer is in step 2.

Q: tan r- sin r 1. Using fundamental identities, simplify the expression sin a 1 2. Using fundamental i...

A: We know that, The trigonometric identities; 1). 1cscx=sinx 2). 1secx=cosx 3). tanx=sinxcosx 4). cotx...

Q: If f(t) -Int find f'(t). Use exact values. 4 16' f'(t) = 2 x o tở In(t)

A: This is a problem of differentiation. Please follow the procedure given below. 

Q: Solve the equation y' + y · tan (x) = sec(x) Ans y sec(x) = tan(x)+c %3D

A:

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer ...

A:

Q: Determine if the series comverges or diverges. If the series converges, find its sum. If it Σ 4n 4(n...

A: This is a problem related to series and sum calculation Based on the available method we will find o...

Q: The daily cost C (in dollars) for a manufacturer to produce a electronic video components is given b...

A: Daily cost for a manufacturer to produce x electronic video components is given by: Cx=1000ln2x2-800...

Q: Find F' (x) if F(x) = L Vt² + 1dt.

A:

Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the in...

A:

Q: Use Bisection Method to find the root of æ + 10x? – 5 0 that lies in the interval (0, 1) to four-dig...

A: We have to find the root of the given cubic equation using bisection method.

Q: Consider the points A(3, –3, 5), B(5, –5, 2), C'(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of...

A: AB→=(5, -5, 2)-(3, -3, 5)AB→=(2, -2, -3)AC→=(-1, -4, 2)-(3, -3, 5)AC→=(-4, -1, -3)AD→=(4, 1, -8)-(3,...

Q: Solve for the antiderivative of the function f(x) = C. *++3x + C A. ++9x+C B. 즉++9x +C D. 2x ++3x + ...

A:

Q: Write the value of lim, 4x2-16 →2 x-2

A: Topic = Limits

Q: a. Consider the parabola f(x) = x² -4x + 3 i) Write the equation in vertex form. ii) Find the vertex...

A:

Q: Example 2: Find the parametric and symmetric equations of the line through the points (1, 2, 0) and ...

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Q: Sketch the region bounded by the curves, and visually estimate the location of the centroid. y = ex...

A:

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z = e...

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used: ddxsinx=cosxddxcosx=-sinxddxenx=nenxProd...

Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2...

Q: What is the common ratio of the geometric progression 3, -6, 12, -24, 48...?

A:

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a din...

A: We use permutations and combinations. Number of ways to arrange n objects in n places is n! Number o...

Q: If f is continuous over the interval [a,b] and F (x) is any antiderivative of f(x) then f(x)dx F(b)-...

A:

Q: (a) The total reserves of a non-renewable resource are 400 million tons. Annual consumption, current...

A: Given: The total reserves of non-renewable sources are 400 million tons. Annual consumption, current...

Q: Evatuate the function at the given value of the independent vaniable. Simplity the results x) -- x) ...

A:

Q: Find the volume of the solid formed by revolving the region bounded by the graphs y=x and y=x' from ...

A:

Q: Use the method of cylindrical shells (for all parts) to set up an integral (without the absolute val...

A:

Q: Given f(x, y) = In Vay³. What is the value of fy (1, 2)? If the answer is a fraction, write your ans...

A: Given:  fx, y=lnx2y3 To Find:  To determine the value of fy1, 2.  

Q: B. What is the derivative of y with respect to x if y2 – x² = 4? Justine Ashley y? – x² = 4 y? = x2 ...

A:

Q: -1 dx 21 16

A:

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

A: f(x,y)=5x+3y2+5 fx(x,y,z)=5fy(x,y,z)=3(2y)=6y∇f =fx(x,y,z) i +fy(x,y,z) j

Q: Compute the volume bounded by y = x² – 2x and 3y + 2x? – 27 = O when it is revolved around the y-axi...

A:

Q: f (x) | f'(x) g(x) | g'(x) -1 -7 16 -4 4 -2 1 -1 1 -1 3 10 11

A: Let's find.