Q5. Solve: = y² (1+x²), y(0) = 1.

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Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) =

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Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A: Given,

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A: Concept: We have a rectangular zone that measures 16miles and 12 miles Let the five buildings in the…

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Q: Graph the rational function. -2x+2 -x+4 Start by drawing the vertical and horizontal asymptotes.…

A: This is a problem related to graph function. Based on the general formula and concept we will answer…

Q: 27. Check whether the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a ight angled…

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Q: 1. For the vectors v = and u = a. Find v-u b. Find ||v|| and ||u|| c. Find the angle between v and…

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Q: Consider the following. x² f(x) = x + 7 Find the derivative of the function. f'(x) = x(x+14) (x+7)²…

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Q: We know that F is an antiderivative of f, so to: O a) lim (F (b) - F(a)) a 0 Ob) lim (F (b)-F (a))…

A: Here given that, F is an antidervative of f, so we have to find the value of ∫0bf(x)dx=?

Q: Derive the Maclaurin and Taylor Series of the function below:

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Q: 3 B 3! - What is the second derivative of the function f(x) = xex ?

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Q: For the function f(x) = 2x³-5x² +11x +3, find f''(x). Then find f''(0) and f''(2). To find f''(x),…

A: The given function is f(x)=2x3-5x2+11x+3

Q: Below is the graph of y= log₂ x. Translate it to become the graph of y= log₂ (x+2)+4. X -6 -4 -2 2 ?

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Q: D Question 15 Find the value of b such that the function f(x) is continuous everywhere. x² + a if x…

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Q: e. The line through (1,1,1) parallel to the z-axis. f. The line through (2,4,5) perpendicular to the…

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Q: Find the exact length of the curve. y = 5 + cosh (2x), 0≤x≤ 7

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Q: = A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y -4x²…

A: Maximize area

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Q: A number x is selected at random from the interval [4,20]. The probability density function for x is…

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Q: For each function, determine whether it is a polynomial function. Function (a) v(x)=3x² +0.6x4 (b)…

A: polynomial can have constants (like 4), variables (like x or y) and exponents (like the 2 in y2),…

Q: 3) Find equations for the lines: h the no e. The line through (1,1,1) parallel to the z-axis. f. The…

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Q: Determine the center and radius of a circle given that its equation is x² + 12x + y² - 6y = 4 Use…

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Q: Consider the following. f(x) = =x+4 (a) State the domain of the function. O all real numbers x O all…

A: We have to find asymptote

Q: If y = ecos(x) then y" + sin(x) y' cos(x)= ***

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Q: The function f is defined as follows. X if x #0 f(x) = 2 if x = 0 (a) Find the domain of the…

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Q: an integral corresponding to the area of the region bounded by the curves of the functions f and g…

A: f(x) =x2 -4x  g(x) = -x2 here area function = f(x) - g(x) = x2 -4x  -(-x2 ) = 2x2 - 4x

Q: Reduce the rational expression to lowest terms. 2p² + 12p+16 2 4p²-4p-80 2p² +12p+16 4p²-4p-80

A: I am attaching image so that you understand each and every step.

Q: If y = ecos(x) then y" + sin(x) y' +cos(x)=

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Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: A utilities company wants to deliver gas from a source S to plant P located across a straight river…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: B3. Find the integrating factor by inspection then solve.  ydx + (x + x4y2)dy = 0

A: Let's solve given diffrential equation.

Q: 79 J ·S= sen7⁹ (x) dx. When applying variable change u-cos(x) 39 ○ a) J = [ (1 − u²) 3⁰ du Ob) J=…

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Q: -4 M -2 2 4 6 (i) Identify the critical numbers of f. (Enter your answers as a comma-separated…

A: Given problem:-

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Q: 4) Find equations for the planes: a. The plane through P, (0, 2,-1) normal to n=3i-2j-k

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Q: Find the equation the tangent line and normal line to the graph of f(x) = √x at x = 4. Graph the…

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Q: Consider the function f(x) = sin(4x). a. Determine f '(x). b. Determine f"(x). c. What is the…

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Q: is: The value of the following limit Lim (cos(x))ou(x)

A: The value of the limit is when x tends to 0 for the function (cos(x))cotx

Q: Consider a spring with constant k= 200 N/m, If the spring is compressed 4 cm, so the integral that…

A: work done in spring    W = ∫kxdx here  k = 200  upper limit in cm  2 and lower limit 4  so in meter…

Q: generated by revolving the given plome area line uning the dirc method. (answers ore in cubic a.)…

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Q: Consider the solid shown in (Eigure 1). Suppose that a 49 in., h-343 in. Figure 1 of 1 x³0 Y Part A…

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Q: Find the average value over the given interval. f(x)=x²+x-7; [0,14] The average value of f(x) = x² +…

A: We have to determine the average value

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Q: Use the table of integrals to evaluate the integral. 6² 3saxav 53x³√4x² - x4 dx

A: To evaluate the integral.

Q: Question 11 Evaluate the limit lim (ln(3x² + 2) - In(x² + 1)) O ln 3 O In 3 01 00 O ∞

A: To evaluate the following limit.limx→∞ln3x2+2-lnx2+1

Q: un J-2√√2+x (c) Let u₁ = x² - y² and u₂ = x³ - 3xy². Show that u₁ and u₂ are harmonic functions and…

A: Solution

Q: B5. Find the integrating factor by inspection then solve.  y(2xy + 1)dx - xdy = 0

A: find out the integrating factor by inspection and then solve the differential equation.