dy dx Using logarithmic differentiation, find NOTE: Express your answer in terms of x only. dy dx = if y= (x² −9)√√x³ +1 x6 - 3x + 5

Q: Evaluate the definite integral 2 Lice (t² + 7) dt? O 28 O 70 O 10 O 24 O All of the above CD Co

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11.

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Q: Evaluate O O O O K|4 2 6 wo|= • S² +2²+1 dt. - 3

A: Here is the solution:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Here we have to check the convergence of given sequence

Q: Find the integration by applying (by part method) f Sin-¹y dy

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Q: The graphs of the functions f(x) and g(x) are shown below. y 11 10 9 8 7 6 85 14 (a) Find (f. g)(2).…

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Q: Q1: Sketch the signals A. x(t) x(-1/2) A CL x(2(1+2)) x(−1+1) Ates Ades 0 2 B. 2 x(t) 0 1 x (3t),…

A: Given data:- Part A=   Part B

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z][-1, -9,16]++[3, 3,…

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Q: Evaluate the definite integral. TT/3 [C [(sec t tan t)i + (tan t)j + (2 sin t cos t)k] dt 10

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: 1. The half-life, T, for a particular radioactive element is 3 min. Find the decay rate of the…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Consider the following vectors á = 2ī+3j and b = -2ī+ 3k and c = −3ī + k

A: topic- projection of one vector on another

Q: f Cos5x dx

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Q: opulation P has doubled in 7 years, how long will it take to triple? (Round your answer to one…

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Q: Identify the open interval on which the function is increasing or decreasing. h(x) cos(쯤), 0 < x <…

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Q: d dx [3 sin³ (tan √x² + 3x²)] d [(x² + 1) cotx dx 3 cos x csc x

A: Given

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: The vertical displacement of an object fired at an initial velocity v and an angle of elevation at…

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Q: A population of 470 bacteria is introduced into a culture and grows in number according to the…

A: Given problem:- A population of 470 bacteria is introduced into a culture and grows in number…

Q: 7. y = (x+1)* 9. y = Inlog, x

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Q: (b) Given that s² + 16 (s − 1)(s + 3) (s² + 4) (s Evaluate the values of A, B, C and D. - A B + 1)…

A: We have to do partial fraction of given algebraic expressions.

Q: The cost, in dollars, to produce xx vats of ice cream is C(x)=6x+12C(x)=6x+12. When selling them to…

A: This question is related to price and cost functions, we will solve it using given information.

Q: Exercise 1.8. Prove (1+2+...+n)² = (1+2+...+ (n − 1))² + n³ by mathematical induction, and discuss…

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Q: identify the equation of the curve that passes through the point (0, 1) and who tangent line has…

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Q: (4) Find the integration by applying (by part method) Sin-¹y dy

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Q: Find the limit. Enter the exact answer. If the limit does not exist, indicate that using the check…

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Q: 5. The points A(1, 0, 2), B(2, 0, 1) and C(1, 2, k) form a triangle of area √6. Determine the…

A: Follow the procedure given below.

Q: R. H. side is 3 2 [ f z=1 y=1 -2(x+1)y dy dz

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Q: Use the formula: PMT= (PV) 1-(1+i)*

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Q: 6. lim x-3 x2+4x+3 x+3

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Q: 4x Compute the values of dy and Ay for the function y = e + 2x given x = 0 and Ax = dx = 0.05. Round…

A: Follow the procedure given below.

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: topic - exponential function

Q: Using horizontal strips, which of the following gives the area of the region R bounded by y=2+x-x²,…

A: Explanation of the answer is as follows

Q: Determine the values where the following function is discontinuous x² + x-3 2x +3 f(x) = if x+6…

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Q: Which of the following conditions is NOT required for lim f(x) to exist? x→a

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Q: Consider the region S shown in the figure below and take note of the following points of…

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Q: What is the cartesian form of the complex number: (-1-i√3)-4

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Q: 1. Determine the area below f(x) = 8x - 2x² and above the x-axis. 2. Determine the area to the right…

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Q: The range R and the maximum height H of a projectile fired at an inclination 0 to the horizontal…

A: Note: Since, in the image of the question posted by the student, it is not clear how many place to…

Q: In the Figure 1, if Q= 40 N, P = 50 N, and B = 145°, then R is equal to (in N): Figure 1: C R A Q B…

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Q: If w = cos(xyz), compute for O-x²yz cos(xyz) - x sin(xyz) -x²yz cos(xyz) + x sin(xyz) O x²yz…

A: This question can be solved using the concept of partial derivatives.

Q: Let R be the region bounded by the line y = 1, the parabola y = x², and the curve y = √√. Find the…

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Q: QuIf w=f(u, aw Prove that əx v) = cos uv, u = xyz ,v= 4(x²+y²) = 0 at the this point (x,y,z)=(1,1,1)

A: w=fu,v=cosuv, u=xyz, v=54x2+y2

Q: Let F(x) = f(x¹) and G(x) = (f(x))4. You also know that a³ = 9, f(a) = 2, f'(a) = 15, f'(aª) = 6.…

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Q: e will examine two procedures in the use of partial integration (See image) a) Procedure 1: Derive…

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Q: Find the derivative using logarithmic differentiation √x+1 y= (x+2) √x +3

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) -1 lim (-6 +h)-¹ + 6-1…

A: L'Hospital rule:- If limx→0f(x)g(x) is of the form 00 then limx→0f(x)g(x)=limx→0f'(x)g'(x)Continue…

Q: Let f(x) = { x - 2 7x 38 Find the following limits. lim f(x) = x→6- lim f(x) = = x→6+ lim f(x) = x-6…

A: This question can be solved using the concept of limits.

Q: 3. Does the parametric equation r = (2,-5,2) + s(1,4,2)+(-2,-3,1), s,/€ R, and the vector equation…

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