Question 9 Evaluate: lim 0 2x 222. None of the choices 1 2 0 -1 +x

Q: (b) If ƒ is continuous on (a, b) then there is a number c in (a, b) such that f(c) is an absolute…

A: Consider the statement  If f is continuous on (a,b) then there is a number c in  (a,b) such that…

Q: Find the perimeter of the triangle with ver an isosceles triangle?

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Q: f(x csc² 2x - x cos x cos 2x)dx

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Q: nverse for the following functions. If it does not exist, show why. f(x)=2x-1 f(x)=√x-3 f(x) = |x-1|…

A: Topic:- calculus

Q: Suppose that the function fis defined, for all real numbers, as follows. x-2 if x < -2 f(x) = 3x+2…

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Q: 4. 5. 1 X√(x)}² (x)²-49 dx 1 √9+8x-x² dx

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Q: Example 3: Find the parametric and symmetric of the line passing through the point (-3, 5, 4) and…

A: Here, the given equation of the line is: x=1+3t,y=-1-2t,z=3+t Therefore, the direction vector is:…

Q: Which of the following vectors is coplanar to [1, 1, 1] and [1, 2, 3]? O a) [4, 2, -2] b) [5, 7, 6]…

A: Given vectors  [1,1,1] and [1,2,3] For coplanar with another vector, the determinant should be zero.…

Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 9) Verify that it is orthogonal to both a…

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Q: find the points at which f has a local maximum or a local minimum

A: This question can be solved using the concept of maxima and minima.

Q: 2x³4 Q1 Investigate the limiting behavior of_f(x,y)=- x4+y² as (x,y) approaches (0,0)

A: Along x=0 f→0y2=0

Q: What is the mass of body if the exerted force of 10 N is accelerated by 5 m/sec^2? O 4.5 kg 1.5 kg O…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: VIP 2 = √ Бхутуг П , Ө от 58 x = CS 0 ) y = Sine -

A: Topic:- application of derivatives

Q: Part One. Multiple Choice 1. Which of the following is not a true statement about limits? a) A limit…

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Q: Option 1: Given sec 0 = where <0 < T. Calculate the exact value of sin cos 0 + tan² 0. Show all your…

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Q: lim √25t2 + 2-5t

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Q: The x-component of a force of 50N is 30N, then what will be the y- component of the same applied…

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Q: Find the rate of change in the area (A) of a circle with respect to its radius (r) when r = 9. 9TT…

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Q: If P(x) is some polynomial then ΣP(n)x" has radius of convergence 1. n=1 Select one: O True O False

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Q: E) If F(x, y, z) = 3x²i + 3zj - 3xk find the Div (Curl F). 0/0 0/0 0/0= az any jaz V-Vx3 = 0₂ 17 Pue…

A: First we find curlF .

Q: Solve the following system: 2x + y - 3z = -3 x + 3y - 4z = 11 x + 8y-9z = 5 (2,-1,0) no solution

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Q: 12 1= A ✩ = OÅ and √ – OẺ . Then, AC is equal to: U= = Oa)-7-7 Ob)-7 Od-+7

A: Topic:- vector algebra

Q: Given the function f(x) = {2ª 2x x 2 which statement is FALSE at x=2? O The derivative from the…

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Q: Consider the following matrix. A = [22 -2] How many vectors are in the basis of row(A)?

A: Given: Now,                   30-3222Reduced matrix to reduced row echelon form:=10-1012The rank of…

Q: Find the derivative of the function 6. g(s) = f (t – t²)³ dt 5

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Q: Q4. f(x)=5 and 1(x)de=8 dx = 5 and f(x) dx = 8 then f(x)dx a) -3 b) -13 c) 13 d) 3 dx is given by

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Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: 7. f (ex + 1)² dx 8. fex dx/(e²x + 3) 9. f (cos x-sin x)² dx

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Q: f is continuous on (a, b) then there is a number c in (a, b) such that f(c) is an abso inimum value…

A: Topic:- calculus    Definition :-  Extreme Value Theorem   If a function f(x) is continuous on a…

Q: - Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x) -1(y/x)

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Q: 5. Find the residues of the following: a. 2-2 z(1-2) at z = 0; at z = 1

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Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

Q: √√3 L dx 1+x²

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Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

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Q: A stone is released with zero velocity from the top of a tower, reaches the ground in 4 sec. The…

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Q: ve for y esec(4y²-6y+14) = 3x + 1

A: We have to solve for y of the given equation

Q: f(x csc² 6x - x cos 6x)dx

A: Given, ∫(x csc2 6x-x cos 6x)dx

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: A particle moves along a straight line such that its displacement at any time (t) is given by…

A: Note: There is a typo in the question.  Incorrect:  S = t^3 - 6t^3 + 3t +4   Correct:  S = t^3 -…

Q: What is the domain of the function f(x)= |x|? 0 (-∞,∞0) ○ (0,∞) 0 (-∞,0) ○ [0, ∞)

A: We need to find domain of given function.

Q: 2dx 2 2 cos x√ 4tanx - tan x S-

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Q: Find the Volume: Rotate the region bounded by y = 7 - x², x = -2 and x = 2 and the x-axis about the…

A: Volume of the solid of Revolution :  Suppose y=f(x) is a continuous non-negative function on the…

Q: Prove that sin²x x cos²x = csc²a-cot²x 4c8c²2x

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Q: Using the Maclaurin series expansion of e, to find the series expansion of f(x). Express [ f(t) dt…

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Q: lim (√x² + 4x +1 − x) x→∞

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Q: Evaluate the integral: 18x² √64 x² - I dx

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² =…

A: Let's find surface area rotated about x=0.

Q: Determine if the improper integral •+∞ dx x ln7 x is convergent or divergent.

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