Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

Q: Starts the domain, vertical asymptote, and end behavior of the function.  g(x) = ln(3x +21) + 1.5…

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁749 dx…

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

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

A: We have to integration

Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

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…

A: We have to find the integral

Q: Find the area of the parallelogram with vertices P₁, P2, P3, P4 P₁ = (1,3,3), P₂ = (1,2,2), P3 =…

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Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t = - dt

A: Given that the differential equation  ds/dt=10*csc^2(2t) Determine by s=2 when t=pai/4  To find the…

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Q: A) Link between plane and line in the differentiation. 7) Find the aquations of alono pocinh the…

A: Link between line and plane.

Q: Area of the Region and Volume of the Solid of Revolution Given: The region is bounded by the curves…

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Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: Given: Now, we find the mentioned ratios. sin A=662+102=6234=334cos A=1062+102=534tan A=610=35

Q: Find the volume of the largest right circular cone that can be incribed in a sphere of radius 3. 3 y…

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Q: ND THE AREA BOUNDED BY THE = x(x-1)², y-AXIS, AND THE =12

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

A: using the simpson's method ∫01xdx for n=4.

Q: Considering C is a curve which has the following parametric equations: 1 t³t+1, C = { x (t) = { 1³3…

A: Parametric equation

Q: [²₂1 (²) Given than [ f(x) dx = 3 Ⓒ ® B Lof(² f (x) dx = = [₁, ƒ (² f (x) dx - f (x) dr 1₁° dx -2 3…

A: Given

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

A: see below the answer and calculation

Q: Find the indefinite integral: O x4+x+C Ox5/5+x²/2+c O x5 + x² + c O 5x5+2x²+c Sx(x³ + 1) dx

A: Given ∫x(x3+1) dxTo evaluate the integral:

Q: 5 dx In evaluating 1 is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=5.91.…

A: ∫ 351x2-9dx

Q: f:R+ → R f is a strictly decreasing function. 3 1 f (x) · f ( f(x) + 2x 4 f (9) = ? 1) 3) 1 6 4) 1…

A: Answer is given below.

Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim 1-0…

A:

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

A: Derivative of cos(x) = - sin(x) We have to find the value of f(x) at x=0.96

Q: Cynthia's investment of $81,200.00 in a fund matured to $160,353.29 in 7 years. If the interest in…

A: We want to calculate period and nominal interest rate.

Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: aces)

A: We will find the value of the integral

Q: Iff is continuous on [a,b], then (A) True B) False b b xf(x) dx = x f(x) dx a a

A: In this question, we want to know whether the given statement is true or false.

Q: Find the area bounded by y = x3 +6, y = x and y-6 www. -X.

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Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

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Q: Consider the vector-valued function 4t-8 [{m(3. In(3-t), 5,31²-8 8 R(t) 4-1² (0, -1,4), 1. Find the…

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Q: Find the equation of the tangent lines and the normal lines to the curve y = √2x-1 at x=5

A: Find the equation of tangent line and normal line to the curve y=2x-1 at x = 5.

Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: Using Trapezoidal method √x²dx for n=4 is equal to Blank 1 (use 2 decimal places with proper…

A: SOLUTION-

Q: Find vertical asymptote, x intercept and y intercept of (x+1)(x-5)/(x-6)

A: Topic = Functions

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

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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: dx x+y cos x 1tsinx Ans: (1 + sin x)y + x² = c

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Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: . The area bounded by the parabola y² + x - 2y = 1, the x-axis, and the line x = 2 revolves about…

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Q: Let (t) = 5 cos(t) and y(t) = 3 sin(t) All answers should be decimals rounded to 2 decimal places.…

A: Applications of differentiation

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: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Let's find initially present bacteria.

Q: Suppose g(x) = x²f(x) and it is known that f(3) = 5 and f'(3) = −2. Evaluate g'(3). gʻ(3) = =

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: Given: planes Π1 : 2x − 5y + z = −1 and Π2 : x + 5y + z = 5 intersecting on a line ℓ. (a) Compute…

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Q: Consider the vector-valued function R(t) = 1. Find the domain of R. 2. Show that R is continuous at…

A: All three questions are solved.

Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: We will use simple trigonometric formulae to solve this question.

Q: Given Cost and Revenue functions C(q) =q³-9q² +57q+5000 and R(q) = -3q² +2600q, what cost is…

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Q: 39 9. A curve with polar equation r = 6sin0+13cose represents a line. This line has a Cartesian…

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Q: 2 ist dx for n=4 is equal to Blank 1 (use 2 decimal places with proper rounding off, no Jo (x + 2)²…

A: Given,  ∫012x+22dx ,  n=4