The distance between -3 and 7 on the real line is 10. ibs O صواب

Q: In(x+2) 1. S dx 2x+4 2 2. fx² ex dx 3. f tan³x dx 12

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Q: Calculate y'. y = ln(x ln x)

A: Given: y=lnxlnx

Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: lim x²e-x x →∞

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Q: a. Find the critical numbers of f on the given interval b. Determine the absolute extreme values of…

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Q: Solve the following. Choose five In(x+2) dx 1. S 2x+4 2. fx² ex dx 3. f tan³x dx 12 dx 1+9x² x-2 5.…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: Question 5 Which of the following is not true? A None of the given choices ℗ √ ² in(x²) dx = I'm √…

A: The objective is to find which option is not true.

Q: xdx (x + 1)²

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Q: Find the length of the arc of the curve y = (1 + x²) fron the point where x = 0 to the point where x…

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Q: (12) Sz sec¹z dz.

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Q: 4. Find the general solution to each of the following differential equations. (a) 2xy² - 1 +…

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Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

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Q: 3. The Critical Point of y = xe-*

A: Answer :-  We have to find the critical point of y = xe-x

Q: lim (lnx) = . x →+∞

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Q: 3 [²(x²) dx 0 Using the definition of definite integral, ff(x)dx= lim f(x) Ax, and the given…

A: Given, ∫03x2dx

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: 5. S Evaluate the integral, if it exists. du √u - 2u² u

A: We have to find the solutions

Q: II. Solve the following problems. Enclose final answer. 4 4. Given z = Find az/ax x+y "

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Q: NT2093E Form a differential equation representing the family of curves 4 a (b + 2y); a, b being…

A: We have to form a differential equation representing the family of curves  3x2 = 4a(b + 2y)  a , b…

Q: Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find a)  The intervals on which f is increasing. b)…

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Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

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Q: A. Determine whether each integral is improper. If it is improper, give your justification. 1² d 4.

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Q: what is Γ(1/2) ? show solution. prove that it is equal to -1/2!

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Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: 4. Determine the area of the region enclosed by y = sinx, y = cosx, x= π/2, and the y-axis.

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Q: x² - 2x² + 3x² -x +3 "x²³ - 2x² + 3 3

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Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

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

Q: 5. Given z = arctan (), Find əz/ay

A: We can answer the question as below.

Q: S (2².1² (2x² – 3x) dx 2 2.

A: ∫252x2-3xdx

Q: Determine whether the following definite integrals converge or diverge and evaluate each convergent…

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Q: |y²Z² YZ Y+ZI z²x² ZX Z + x = 0 x²y2 XY X+YI

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Q: II. Solve the following problems. Enclose final answer. 4 4. Given z = Find az/ax x+y "

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Q: = In ( ²² +2²³v-_-²³ ) · then x +y is da by x-y If the function u = ln

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Q: Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find d)  The open intervals on which f is concave…

A: Given problem:- Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find   d)  The open intervals on…

Q: 3. The Critical Point of y = xe-*

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Q: 5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under Prove your…

A: Given; ( 4D^3-13D+6)y=0

Q: A street light hangs 24 ft above the sidewalk. If a man 6 ft tall walks away from the light at the…

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Q: Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found…

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Q: General solution of (x²y³ - 11) dx (x²y³²) dx + x³y²dy = 0 1+9x², General solution of dy = tan²(x +…

A: This question is related to differential equations, we will solve it using given information.

Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

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Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

A: From Newton’s Law of Cooling, we know that: T(t) = Ts + (To – Ts) e-kt Where, t = time, T(t) =…

Q: 3. The Critical Point of y=xe*

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Q: 32 Remove parentheses and simplify: [4(x + 3) - 4x] -4(x + 3) 4x A O -2x BO 2co -4x-Da

A: Let's simplify.

Q: 7. The particular solution of (D³ - 5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

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Q: 1 Lim x→0* x0x 1 sin x

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Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: Find -x-1 lim 1-0 I² O does not exist O-1/2 O 0 O 1 O 1/2 O Other:

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Q: 4 2 ["S² sinπTy ³ dydx

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