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Q: The differential equation (1 + y')sin(x +y) = y' is transformed into a seperable differential equati...

A: The given differential equation is  (1 + y')  sin(x+y) =y' .. .... (1)

Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent l...

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: The graph of f is shown. State the signs of f′ and f ″ on the interval (0, 2).

A: according to given graph f'x>0 for x∈0,2  now, given curve is concave down and we know that for c...

Q: Based on the graph given, determine f and f'. Justify your answer.

A: 9. Consider the given graph with 2 curves. The red curve has 2 troughs which corresponds to local mi...

Q: Let f(x) = √(x - 3) and g(x) = √(x + 1). Find : (f + g)(x)

A: Given: fx=x-3, gx=x+1 for finding f+gx, we add both functions

Q: You invest in a new play. The cost includes an overhead of $30,000, plus production costs of $2500 p...

A: Consider the given: Fixed Cost = $30000Cost per performance = $2500Sold Out performance brings = $31...

Q: Find the linearization of ƒ(x) = √1 + x at x = 0

A: Consider the following function: fx=1+x Differentiate fx with respect to x: ddxfx=ddx1+xf'x=121+x

Q: If y = 4 - x2, find the value of y that corresponds to values of x for each integer starting with -3...

A: We have given equation y=4-x2. We have to find the value of  y that corresponds to values of x for e...

Q: Why might an integral found in a table differ from the same integral evaluated by a computer algebra...

A:   Integral found in a table differ from the same integral evaluated by a computer algebra system as ...

Q: The region enclosed by the given curves is rotatedabout the specified line. Find the volume of the r...

A: Consider the given function x=y

Q: What is the displacement of an object that travels at a constant velocity of 10 mi/hr for a half hou...

A: Consider the given information 10mihr for a half hour and  20mihr for a next half hour and 30mihr fo...

Q: Graph: f(x) = 2x/3 - 2.

A: The given function is , fx=2x3-2 Let us denote the function fx as y, Now locate the points to draw i...

Q: Identify the two series that are the same.

A: We have to find which series are same. We have given series ∑n=2∞-1nn-12n-1∑n=1∞-1n+1n2n∑n=0∞-1n+1n+...

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: The region bounded by y=x2 and y=6x-2x2 is The cylindrical shell is ∫ab2πxfxdx 

Q: Determine the (largest possible) intervals on which the function ƒ1x2= 2x2 - x4 (as shown) is one-to...

A: according to given graph, given function is one-to-one in x∈-∞,∞

Q: This is on the topic differentiation. I dont understand the method to find solution for these questi...

A:

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

A: The given function is fx, y=xy subject to x+y=10. Let Fx,y=xy+λx+y-10. This implies that, Fx=0∂∂xxy+...

Q: Question 16: May I get just answer of the following MCQ?

A: a (4/211/2), (1/211/2), (-2/211/2) Given that,  Coordinates of Origin, O = (0, 0,0)  Coordinates of ...

Q: Explain why dz r dr dθ is the volume of a small “box” in cylindrical coordinates.

A: (r,θ,z) are the cylindrical coordinates; here r, θ denotes the polar coordinates of the image of poi...

Q: Add or subtract as indicated: [3x/(x - 3)] - [(x + 4)/(x + 2)]

A: The expression is 3xx-3-x+4x+2.   Solve. 3xx-3-x+4x+2=3xx+2-x+4x-3x-3x+2                            ...

Q: Graph the ellipse x2/25 + y2/4 = 1. Give the location of the foci.

A: the equation of the ellipse is x225+y24=1 we have to graph the ellipse. we have to give the location...

Q: Solve the following differential equation . check following Equation can be solved by the method of ...

A: Given, y''-8y'=e8x

Q: If a rock is thrown upward on the planet Mars with a velocity of 10 ms, its height in meters t seco...

A: Given- y=10t-1.86t2 and the velocity v=10 m/s. To find- The average velocity over the given time int...

Q: In order to solve 2x2 + 9x - 5 = 0 by the quadratic formula, we use a =______ , b =________ , and c ...

A: The general form of the quadratic equation is, ax2+bx+c=0.   Compare 2x2+9x-5=0 with ax2+bx+c=0. Thu...

Q: Categorize the following functions as either an " even " fuction or " odd " function of t. Provide v...

A: 1. To categorize whether the following functions are even or odd function. Definition: Even function...

Q: Below are drawings of a wide and a narrow cylinder. The cylinders have equally spaced marks for meas...

A:

Q: Simplify exponential expression. 8x20/2x4

A: The given expression 8x202x4   Exponent rule: xaxb=xa-b

Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression g(5π/6 + π/6) ...

A: Given functions - f(x) = sinx                .........(1)g(x) = cosx          ................(2)h(x...

Q: - Net Change Find the net change in the value of the function between the given inputs. 41. g(1) = 1...

A: The given function is  gt=1-t2

Q: a. Lizards are cold-blooded animals whose temperatures roughly match the surrounding environment. Su...

A: The function is Tt=-0.009t3+0.285t2-1.7t+17.5.   Differentiate the function with respect to t. ddtTt...

Q: Solve initial value problem  y' = 3x^2 - (1/x^2) , y(1) = 5

A:

Q: Two forces, F1 and F2, of magnitude 30 and 60 pounds, respectively, act on an object. The direction ...

A: Calculate the vector F1. F1=30θ1=10°F1=30cos10°,30sin10°=29.54,5.209 Calculate the vector F2. F2=60θ...

Q: Fill in the blank/s: The notation a34 refers to the element in the ________ row and ______ column of...

A: Fill in the blank/s:  The notation a34 refers to the element in the ________ row and ______ column o...

Q: Find the limit (if it exists). If the limit does not exist, explain why.          lim               ...

A: Using path definition of limit we can say limit does not exist.

Q: Arc length Find the length of the curve 3 x² + y V3 -sin from x = 0 to x = 1. V3

A: y=x23-x2+32sin-1x3 Differentiating with respect to x, we get dydx=12dxdx·3-x2+d3-x2dx·x+32·11-x32·dd...

Q: Find general solutions of the differential equation  x^2y'=xy+3y^2

A: Consider the given: x2y'=xy+3y2 Homogenous equation therefore, substitute y=vx and y'=v+xdvdx. v+xdv...

Q: Limits Evaluate the following limits or determine that they do not exist.

A: Given limit expression - limx,y,z→3,4,7x+y-zx+y-zlimx,y,z→3,4,7x+y-zx+y-zRationalizing with numerato...