Find the area of the region bounded by y² = 4ax and x² = 4ay.

Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

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A: ∫-11x7-4x9+sinx1+x22dx

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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Q: Given than f(x) dx = -5 and [² 1 (² A [² f (x) dx + ₁²5 (2²) dax = 0 f(x) ® √₁² f(x) dx = 8 B © f…

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Q: Using Simpson's method √√√x dx for n = 4 is equal to Blank 1 (use 2 decimal places with proper…

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Q: For the function y =f(x), it was found out that f(c) = 0. What can be said that x=c? O critical…

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Q: . Compute for the relation between the cubic inch and the cubic cm by taking the ratio of the volume

A: 1 inch = 2.54 cm    1 cubic inch  = (1 inch × 1 inch × 1 inch)  = (2.54 cm × 2.54 cm × 2.54 cm)  =…

Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x² - X…

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A: We know the compound interest formula:A=P1+rnntwhere A=Principal amount +interest Amount…

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A: The integration of the integral is |2x+1| limit from -2 to 2.

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A: We have to find out the option

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Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).

Q: Evaluate J (2a² y +9y³)dA, D is the region bounded by y www 33522 a. 5 O b. 4811 5 OC. None of the…

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Q: If 2x²+x+1 S (x-1)(x+1)(x-2) A -2 B None 11 3 U D E - 3 11 3 A SA -dx = B + x-1 x+1 x-2 с -+ dx,…

A: Given, 2x2+x+1x-1x+1x-2

Q: 7 x = R¹, ƒ(x):=· + 3√x² 1-x 1+x² +ea² +1 +π².

A: see below the answer and calculation

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Q: In evaluating 2 dx 5₂₁²= is same as evaluating lim_cos-¹(f(x))|c. Determine the value of f(x) if…

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Q: Solve for x. O-1,-4 O -1,4 O 1,4 O 1,-4 x-1 3 2 x-2 =0

A: Given,      x-132x-2=0

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

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Q: Using Trapezoidal method Blank 1 0.34 2 So dx for n=4 is equal to 0.34 (use 2 decimal places with…

A: Given ∫012(x+2)2 dx To evaluate integral using Trapezoidal Rule:

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A: Let's find distance traveled by a particle.

Q: Using Simpson's method Blank 1 Add your answer √xdx for n=4 is equal to Blank 1 (use 2 decimal…

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Q: Why did you take f'(x)=0 and from them I didn't understand, can you explain it a bit, its really…

A: We have to explain the term f'(x)=0.

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂ : r = 2-2 sin (in red) and let R be the…

A: Let's solve. Two curves given r=3 and  r=2-2sin(theta).

Q: Question Find the area A of the region that is bounded between the curve f(x) = 4 sin (4) g(x) = 4…

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Q: vy B. Find the derivative of function f(x, y, z) = 3e* cosxy + ex² + Inzx at point P(1,0,) in the…

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Q: A B D 0 Consider the integral f sin ¹x dx. If we let u = sin ¹x and dv = dx, the integral can be…

A: We have to above question

Q: Given than an f* f (x) dx = -4 and Ⓒ ²1 (2) dua - [² 31 (2) dir = A f 3f dx 22 B [₁ f (x) da = 6 0…

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Q: x6 cos(x³) A) True B) False |dx=0

A: We have to check by even or odd function

Q: If you evaluate the integral expression 12x+1|dx the result is Blank 1 (use fraction or decimal in 2…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for [x(t) =…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin (2x - 6) sin(4x12)…

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Q: II. Find the sum of the following convergent series. lim = = = lim lim 0-2 1 [tan ² (2n-1) - tan²¹…

A: Given problem:-

Q: A CD has diameter of 120 millimeters. When playing audio, the angular speed varies to keep the…

A: Use velocity relation with angular velocity

Q: Using Trapezoidal method proper rounding off).64 √√x dx for n=4 is equal to Blank 1 (use 2 decimal…

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Q: If you evaluate the integral expression |2x - 3|dx the result is Blank 1 (use fraction or decimal in…

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Q: State the domain, vertical asymptote, and end behavior of the function. g(x) = ln (6x + 12) + 1.3…

A: Domain of a function:-  Set of all values of independent variable such that function at that point…

Q: Find the value of C so that the function is a density function. f(x) = [Cx¹ if 0≤x≤ 9 10 otherwise

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Q: xdy = (5y + x + 1)dx Ans: y

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Q: (b) f is concave down on (-∞, 1) and concave up on (1, ∞). (c) lim f(x) = -∞ and lim f(x) = ∞. x-1-…

A: As per the guidelines we can solve 3 parts only

Q: Find f. f(t) = f"(t) = 5et + 6 sin t, f(0) = 0, f(T) = 0

A: On solving this we will get