Q2: Solve the following integral (1) 7x²+14x+15 (x²+3)(x+7) dx dx ; (2)

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

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Q: 인 여 प्रि sin K K K

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Q: y"+y=t y'(0) = -2 y(0) = 1

A: The differential equation is given by      y'' + y = tThe auxiliary equation of the corresponding…

Q: nd the limit (if it exists). (If an answer does not exist, enter DNE.) 15 lim (x,y) → (0,0) x6y²

A: To  find the  limit.

Q: The answer above is NOT correct. Find the area of the region enclosed between y = 4 sin(x) and y = 3…

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Q: The velocity function the time interval [-3,5]. article moving along a line. Find the displacement…

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Q: Q4: Answer two only: 4 2 2 1 -1 1 (A): If A = -2 Find AB and AC. 01 0; 2 B = 2 -1 3 -2 -2 and 2 1 3…

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Q: When a patient with hypertension takes a particular type of blood pressure medication, the effects…

A: We have to find the interval in which interval will the systolic pressure be lowest.

Q: Consider a linear system (a) (b) 2x + 3z = k²2 - k-6 3x - 2y = k²-9 x + 2y + 6z = 2k - 6 For what…

A: A linear system is said to be homogeneous if all the constant terms are zero.

Q: 7. 0 , e5) a dx

A: Please see the below picture for detailed solution.

Q: Compute the partial sums S2, S4, and S6 of 1 1 + 5.6 6.7 (Use symbolic notation and fractions where…

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Q: sin 8 cose √cos²0-9 c. f S do

A: Since, we have been asked to solve Part-C in which we have to evaluate the integral given…

Q: A particle moves along a straight line from the origin (O) with an initial velocity Va=6ft/sec and…

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Q: Sketch the space curve. Function r(t) = (5 sin t, 3t, 5 cos t) 1.0 0.5 0.0 0.0 -0.5 -1.0 -5 N 0.5…

A: Please see the below picture for detailed solution.

Q: Consider the following situation, which involves two options. Determine which option is less…

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Q: Solve using variation of parameters: y" - 2y + y = e/(1+1²) + 3et Type the letter of your answer. Yc…

A: Follow the procedure given below.

Q: Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then…

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Q: Find all critical points of the function g (0) = sin² (120). Express your answer in terms of . (Use…

A: This question is based on general solution of Sine function.

Q: dy dx Q5: Find for the following functions: (2) y = tan³√√cot(7x);

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Q: You have a moment vector, M = [ 219.2 i + 270.5 j + 211.9 k] lb*ft and unit vector, u = 0.4286…

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Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→2…

A: The limit is evaluated below.

Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

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Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞ x / √x^2+x+1

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

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Q: 10.¹ (3x² - y²) dx + (xy − x³y¯¹) dy = 0 2 du

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Q: aluate the following integral in spherical coordinates. This integral calculates the volume of the…

A: See this solution in below

Q: Given the space curve r(t) = (2 cos 2t, 2 sin 21, 31), find the unit vectors, 4 B

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Q: Example Two tanks T₁ and T₂ each contain 100 gal of water each. In T₁ the water is pure, whereas 150…

A: AS WE KNOW THE GENERAL FORMULA IS dy1dt=inflowminconcentration of…

Q: Describe the level curves of the function. z=x+y, c= -2, 0, 2, 3 O The level curves are parabolas.…

A: We need to choose correct option.

Q: If f(x) = 1/√x, use the definition of the derivative to find f'.   You must show ALL of your work…

A: The given problem is solved below in detail.

Q: (4) fxe-x dx

A: We solve this integral using integration by parts method .

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: The volume of the solid obtained by rotating the region enclosed by y = 1/x³, y = 0, x = 3, x = 4…

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Q: -2 S² g(x) dx -6 if g(x) is an even function.

A: We need to evaluate integral.

Q: Find the exact length of the curve. y ‹ = ²(1 + x²j³/2₁ 3/2, 0≤x≤ 5

A: The objective of the question is determine the length of the given curve.

Q: The interest on an account increases exponentially. If an initial investment of $5000 earns $900 in…

A: Given: Initial amount =$5000 Increase amount =$900 Time =2 years To find: Rate of increase at the…

Q: For f(x) = 7x and g(x)=x+4, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.…

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Q: y = sin(x), y = 0, x=0, x= π Exercise (a) the volume of the solid formed by revolving the region…

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Q: Compute u v if u and v are unit vectors and the angle between them is

A: topic- dot product of vectors

Q: 4. 4 1 [x²ydxdy 20

A: I have stated the used formula in the solution

Q: cos θ = 5/13 , θ lies in quadrant IV Find sin 2θ.

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Q: 900mL of lactated ringers is infusing at a rate of 42gtt/min.  The drop factor is 60gtt/mL.  How…

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Q: Use logarithmic differentiation to find the derivative of the function f(x) = (sin 7x)/x c) Coal is…

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Q: The volume of the solid obtained by rotating the region enclosed by y = x = 1, x = 7, y = 0

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: The given set,     S=1,2,3,4, 1,0,1,2,3,8,11,14

Q: J 4 sin xecos* d.c

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Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: t) The volume of the solid obtained by rotating the region enclosed by y = 12x - 4x², y=0 bout the…

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Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤y≤16, 0≤z≤ with √√y density…

A: To setup and evaluate the triple integral for mass of the box.

Q: 2) Consider the DE: y" + 25y = 0 A) Verify that y = C₁ cos 5x + c₂ sin 5x is a solution of the given…

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