1. Find the area of region bounded by the curves y = x² and line y=x. %3D

Q: If f(x) = (4x – 2)² - (3x² + 6)", find f'(4).

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Q: dx Using Trigonometric Substitution find f(0) 3 (x² + x + 1) 2 4 3 sec? e O 3 sec? e 4 O 3 sec e 4 3…

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Q: What are the domain and range of functions? a) f(x) = cos^(-1) (In(tan x)) b) y= In( (x+1)/(x^(3)+1)…

A: A)f(x)=cos-1lntan xdomain of inverse of the function -1,1.-1≤lntan x≤11e≤tan…

Q: (1 + 2x)e*dx, Using integration by parts and letting Given: u= -1 - 2x, dv = f (x) dx, then the…

A: The given integral,     ∫0∞1+2xex dx

Q: Compute the surface area of the cone generated by revolving c(t) = (t², t) for 0 < t < 4. (Use…

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Q: Find the polar equation of the line y = 7x + 5 in terms of r and 0. (Use symbolic notation and…

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Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: Q2/ solve the Differential Equation [ (2xy+3y²)dx = (x² + 2xy)dy ]

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Q: 7. S 8x³ e** dx il ww be 7dx 8. J sec x esinx bne

A: I am attaching image so that you understand each and every step.

Q: discuss and sketch the graph of the given function f (x) = e" + x %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 3. A water tank has the shape of an inverted circular cone with base radius 4 m and height 8 m. If…

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Q: Ca

A: ∫92-x22dx=∫81-x22dx=∫ 6561-162x2+x4dx=∫ 6561dx-∫ 162x2dx+∫ x4dx=6561x-54x3+x55Add a constant to…

Q: 5. Let f be a function satisfying the following properties: continuous on R \ {0} • f(-1) = -3 •…

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Q: Is this statement true or false?

A: Given a continuous function f on a closed interval [a, b] and f(a) &gt; 0 and f(b) &lt; 0 or f(a)…

Q: cos x Given: tan x dx. Using trigonometric transformation , the integral in terms of u is sin x Cos4…

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Q: Evaluate the definite integral 3e-0.05r dr by the following steps: (a) Determine the indefinite…

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Q: Given the area  in the first quadrant by x^2 = 8y, the line x = 4 and the x axis. What is the volume…

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Q: x³ – 4x – 1 = 0 3 Consider the implicit curve throughout this problem. Find dy/dx and use this to…

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Q: 2х — 5 lim 4x

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Q: Determine the speed along a parameterized path s(t) = (9t³, 7t²) at time t = 6 (assume units of…

A: Given problem Determine the speed along a parameterized path s(t) = (9t3 , 7t2 ) at time t = 6…

Q: r1/2 x2 dx is F(b) – F(a), where Fla) and F(b) are real numbers. What is the value of F (a)? The…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t’i + t°j 70 t4 K(t) (4 + 49 t10)ž

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Q: Find the area A of the part of the circle r = 13 sin(0) + 13 cos(0) in the fourth quadrant. (Use…

A: Here we have to find the area A of the part of the circle r in the fourth quadrant.

Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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Q: Find all points (x,y) on the graph of y = x-4 with tangent lines perpendicular to the line y = 4x +…

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Q: Find a and b in Va+4x-5 dx = x+2

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Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

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Q: 1/2 x2 The result of dx is F(b) – F(a); where F(a) and F(b) are real numbers. What is the value of F…

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Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 31.…

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Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

A: Given integral is ∫x2-x2-1 dx.

Q: Because of an insufficient oxygen supply, the trout population in a lake is dying. The population's…

A: The population's rate of change can be modeled bydpdt=-130 e-t30, where t is the time in days.

Q: The curves described by the following polar equations intersect at which value of the angle theta?…

A: We will put these polar equations equal and solve for the angle.

Q: dx If x2 - 2x - 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Find the general (real-valued) solution of the following differential equations. If an initial…

A: Here, the given DE is: (3x-2y)+(y-2x)y'=0...(1) And, the initial condition is not given. So, the…

Q: dh _10. A cylindrical piston with fixed radius r = 3 cm is being compressed so that How h =- dt fast…

A: Given

Q: Given: dx x3 Using trigonometric substitution , solve for the integral form in terms of 0. A sin? 0…

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Q: Compute the derivative of the given function. log3 x f (x) = %3D cot x - 2x2

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Q: (Ca' - x*

A: we know that,           integration of xn dx = xn+1n+1.  and x-y2= x2+y2-2xy

Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

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Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7

Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: Put 3s+4 (s-2)(s²+7) in partial fractions.

A: Inverse laplace transform of 3s+4s-2s2+7

Q: Find the indicated derivative. f (x) = x² In x + sec a; find f"(x).

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Q: Find f. f"(x) = 6 + 6x + 24x2, f(0) = 2, f(1) = 12 f(x) =

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Q: A 10-foot ladder is standing vertically against the side of a building. To show you a related rates…

A: We can solve as follows

Q: cot ve csc² Ve do 3 Vo (4 + cot? Ve)

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Q: 5. sin (2x) dx

A: To evaluate: ∫sin22xdx ⇒I=∫sin22xdx We know that 1-cos2x = 2sin2x

Q: d太 2.

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Q: Let R = {(x, y) ER214 < x? + y < 9}. By inverting to polar coordinates: %3D y? %3D Vx? - + y2 Select…

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Q: 2. Jx2Vx3 – 27 dx -

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…