10 40 What does that mean 11 Suppose f(x)dx : f(x)dx is equal to? 10

Q: Instructions: (I) Use Limit Laws to find the limit of each given problem. (II) You may only use…

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Q: Find the general solution of ydy/dx =2/(3x²). O a. y? = -4/3x + C O b. y?/2 = 2/3x + C O c. y²/2=…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 au. (v x w)| to determine…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution is given below

Q: Write the standard basis for the vector space using x. (Enter your answers as a comma-separated…

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Q: Does g(t)=3t^5+10t^4−30t^3+70 have any inflection​ points? If​ so, identify them. An inflection…

A: The given function is: g(t)=3t5+10t4-30t3+70 And, the derivatives are:…

Q: Find all real numbers x that satisfy the following equation. 4x ( 1/2 )9x  =  8

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Q: (1) Find the equation of the curve given the slope of its tangent line (mr) and the point P(a,b)…

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2* – x has a critical number…

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Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) 00 E…

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Q: dx 6. xVa² - x² X

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Q: Find the intervals on which fis increasing and the intervals on which it is decreasing. f(x) =…

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Q: 13 dt 9+6t 4 (9+6t)5

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Q: Find an equation of the plane that passes through the points (2, 4, 1), (2,2, –4), and (-–3,5, 3).…

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Q: Use logarithmic differentiation to find dy/dx. x² – 4 x2 + 4 - y = x > 2 dy dx II

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Q: If x is the number of thousands of dollars spent on labour, and y is the thousands of dollars spent…

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Q: Given the plane i = (-2, 1,5) + s(3, -2,0) + t(1, 1, 5), s,t € R. The plane cuts the x, y and z-axes…

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Q: where k > 0. 4. s(s-k)'

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Q: X Your answer is incorrect. Find an equation of the plane that passes through the points (-2, 1, 1),…

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Q: Use the method of reduction of order to find a second solution of the differential equation 1?y" +…

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Q: [x² In x dx

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: We will use the given formula of volume to find the volume of the tetrahedron.

Q: 4. A particle is moving in a straight line and its distance s, in meters, from a fixed point in the…

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Q: Calculate the area of the circle r=18sinθ as an integral in polar coordinates. I have this…

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Q: Find F (x). F(x) = sin e de Jo F '(x) =

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Q: Prove the identity sin x cos²x+ sin?x algebraically and CSC X determine the non-permissible values…

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Q: Logistic population model is given by d P/dt = 10 P (0.2 – P/5000). Analyze and show how this model…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: We need to find directional derivative.

Q: y = (x+6)(x+8)® (x+3)³(x+5)5 Differentiate using Logarithmic Differentiation

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Q: Consider the following function. f (x, y)  =  (x − 4) ln(x6y) (a) Find the critical point of  f.…

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Q: Suppose f(-1) = 3, f'(-1) 2, and g(x)= r'f(2). The tangent line to g(r) atz= 1 is given by Y

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Q: Consider the points A(3, –3, 2), B(4,–5,0), C(-1, –4,0), and D(6, 2, –3). (a) Find the volume of the…

A: AB→ = i -2j-2kAC→ = -4i-j-2kAD→ = 3i+5j-5k Volume of parallelepiped with AB→, AC→ ,AD→ as adjacent…

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: 4- -3 -2- -4+ Use the graph to find the following. If there is more than one answer, separate them…

A: Given query is to find the value of local maximum and at what value of x it's maximum.

Q: 4y" + 25y = 0, y(0) = 3.0, y'(0) = -2.5 %3D %3D %3D

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Q: The profit function for a product is given by P(x) = - x +5x +400x – 1600, where x is the number of…

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Q: please

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Q: 16 sin?x 5. The integral S dx is equal to (useful identity double angle identity for sin) cot2 x+1 1…

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Q: Type exact answer only. No other unnecessary symbols or words. Write DNE if your think the limit…

A: Here we have to find the limit when x tends to '-2' , '0' , and '3'.

Q: Write the equation in spherical coordinates. (a) z? = x² + y² (b) x² + z² = 9

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Q: 4. s= dx = In]x| – e* + C %3D - ? S 2+3*dx = 4 + C In 8 5. S(D- dx =: 32x Inlxl + C 6. 3x. 2 In 3 3

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Q: Money deposited in a fund triples every 8 years. If the bank compounds the interest continuously,…

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Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

A: Solution: Let u = ai+bj makes an angle of 45 degree with v = 9i +4j

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

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Q: Use the union rule to answer the question. If ​n(A)=8​, ​n(B)=9​, and ​n(A∩​B)=4​, what is ​n(A∪​B)?

A: Formula: n(A∪B) = n(A)+n(B)-n(A∩B)

Q: S sin x In(cos x) dx

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Q: In -dx x²

A: This is a problem of integration. Based on the general formula of integral by parts we will solve…

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: 1 Integrate: S tan*÷x dx 3

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Q: 3. [3x*(Cos x² + 6)

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