3. If ƒ(x) = log₂(−(x − 6)) and g(x) = √(x + ²) a) Determine the domain of g(x) + f(x) b) Is there a difference between the domain g(x) + f(x) and f(x)+ g(x)? If yes, state the domain of f(x) + g(x)?

Q: +∞o Evaluate: S e-x dx 0 A + ∞ (divergent) B 0 C 1 D) None E e

A:

Q: y=x², y = 1, y =9 y=9, first quadrant

A:

Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries. 16-y²…

A: Q=∫-44∫016-y2∫0y+6y2z dxdzdyS is the solid of integration of the integral Q.Sketch S and label its…

Q: y = (2x − 1) (x + 4)

A: To evaluate and to solve the function using the product and quotient rule of differentiation.…

Q: ff" (x+5) dx=14, then the value of b is equal to (A) 4 B) 3 (C) -3 (D) None

A:

Q: Evaluate efsin(1 sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression…

A:

Q: dx e* + e* +ex 5. ・ So =

A: We can find the answer as below.

Q: St dx tan 1²dt=2x tan x² X (A) True B) False

A:

Q: -f(x)=√√5x² +2

A: Please see the answer below.

Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: (5x²+4)

A: ddx15x2+43

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A: Topic = Derivative

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A: Given :(x+5)2=2y, the x-axis, and the line tangent to the circle x2+y2=25 at (3,4).To find :The area…

Q: How do you multiply cube in an equation?

A: Solution

Q: 18. f(tan 2x + cot 2x)² dx

A:

Q: S- (A) True B) False tan r²dr=2x tan.x²

A:

Q: dx (x-3)² (A) None B 0 C ∞o (does not exist) - 1 1 S Evaluate: D E

A:

Q: Which of the following equations correctly states the Product Rule of Differentiation? dy = = f(x)g…

A:

Q: Let D be the portion of z = 2z + 5y inside z² + y² = 1, oriented up, and let F = (y, z, -z). Compute…

A: We have to compute integral.

Q: Consider the triangle with vertices P(3, -4, 0), Q(4, -1, -2), and R(8, -3, -3). Determine the…

A:

Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

A:

Q: 1. Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x.

A:

Q: b If ff" (x+5) dx = 14, then the value of b is equal to (A -3 B 4 C 2 D 3 E None

A:

Q: 9. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters)…

A: We need to find velocity.

Q: the correct steps to evaluate cos²20 dº is 0 One of Ⓒ[-[²04 A de sin²20d0 0 0 [1²4] B de- cos 40d0…

A: We use double angle formula  cos(2x) =2cos2(x)-1  cos2(x) =(1+cos(2x))/2

Q: 7 dx x4 - 16

A:

Q: 20. S dr √3-4r-r²

A: On solving this we will get

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A: We will solve the given integral using simple Integration rules.q

Q: ‹S- A S Ⓡ /- © /- S- D For dx and using the substitution = x1/2, the resulting integral takes the…

A: Just use the substitution and find the required integral. Option (B) is correct.

Q: X+2 √4x-x² 16. S dx

A:

Q: Evaluate: 2 sinxcos³xdx is equal to 0

A:

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A:

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A: We have to evaluate ∫4x-2 dxx3-x2-2x.

Q: A ream of 500 pieces of 8½ inch by Il inch copy paper has a volume of 280/2 inches³. What is the…

A:

Q: 4. f ta tan x sin xdx

A:

Q: t'dt √4+1² 19 dt

A: We have to evaluate ∫02t34+t2dt.

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

A:

Q: 5. 4 f sin + 2zdz

A:

Q: 3. Find the average value of the function on the given interval.

A:

Q: 100t Consider the population function p(t) = t+9 a. Find the instantaneous growth rate of the…

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Q: Find the value of integration of Semi-deviant manner when y-n found the real integration facilities…

A:

Q: Stoe 0 ex dx Evaluate: A 0 (B) e (C) + ∞ (divergent) D 1 E) None

A: ∫0+∞e-xdx here ∫e-xdx =  -e-x

Q: f(x)=(5x² +8x)

A:

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: POT Q3.If f(x,y) = sin'(x-3y) +sin xind: of af and ду

A: Given:     fx,y=sin2x-3y+sin-1xy Taking partial derivative with respect to x.…

Q: Rearrange lim x* so that we can apply x→0+ L'hopital's rule.

A: Given,limx→ 0+xx

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A: Given that…

Q: Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ − x + y = 0 (b) x…

A: 4x3y2+x4y3-x+y=0Differentiating both sides and isolating y' we…

Q: Covered topics are Applications of Definite Integral: Plane Areas and Areas Between Curves and…

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Q: 11. J√e²-1dx

A: We have to evaluate the integral.