10- 7-12√ 3 √√9 А. 3 B. V3 О А о B О с D 11 С. 1 D-I

Q: 8- The simple expression of the 7 bs ca 3 a³ 7 bs c A. B. 3 as 21 a³ b³ c 3a³b²c² C. is 7 b5 c 3 a5…

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Q: Activity 1. Determine the antiderivatives of the following functions. 1. f(x) = (x + 1)100 2. f(x) =…

A: 1. fx=x+11002. fx=x2+x102x+13. gx=x31-x4 Note:    Multiple parts are given, we are answer only three…

Q: Find the first three terms of Maclaurin series for F(x) = In (x+3)(x+3)²

A: A Maclaurin series is a special case of a Taylor series, obtained by putting x = 0 i.e.,

Q: i. Using Desmos graphing software or Desmos graphing mobile, create the graph of the following limit…

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Q: 8. Consider an object moving along a line with velocity v(t) = 6t2 - 12t with t measured in seconds…

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Q: Which of the following is equal to e² +c + c +c In(x) + c e dx? da

A: evaluate the following integral... ∫ex dx

Q: n°xf(x) dx = x₁ If f is continuous on [a,b], then A) True B) False <f(x) dx

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Q: Let y = f(x). Which of the following statement is TRUE? O None of the above O Let f(x) = -2x + 4. If…

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Q: 1 If A 1 2 32 O True O false is a matrix then A¹ = [1 3].

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Q: C. Graf the function of y-5x" if n=3 1. O 1 2 2. y = ax",

A: let see how the graph of y =5x3 looks like

Q: y dx y = 9x+8 Find dx

A: The given function is: y=9x+8   As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Rule:…

Q: IF Y = u²-1 u²+1 Find dy np

A: Given,  y=u2-1u2+1

Q: Show that the equation is homogeneous and find its solution. dy/dx = x+3y/x-y

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Q: A rocket is propelled vertically upward from a launching pad 150 metres away from an observation…

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Q: Consider the circular helix with equation R(t) = (12t, 5 cost, -5 sint). (a) Find the value of t…

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Q: 5. How is -28 can be express as rational number with numerated the number 4? 84

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Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

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Q: Find dy and simplify whenever possible. 1. y=(5-6x)¹2 4x-5 2. y=--- 2x + 1 3. y=(2x+5)(4x−1)

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Q: The equation of a hyperbola given below when reduced to standard form is 16y² -9x² +36x +96y - 36 =…

A: solution:-16y2-9x2+36x+96y-36=016y2+96y-9x2-36x-36=0  to make perfect…

Q: Find parametric equations for the sphere centered at the origin and with radius 8. Use the…

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Q: Finding the rate of change of the function defined by y = x³ and evaluating it at x=9 units yields…

A: topic - rate of change of function

Q: Find the 2nd and 3rd derivative of the function y'= 3x^2y^2 with respect to dy/dx

A: Find the 2nd and 3rd derivative of the function y'=3x2y2with respect to x

Q: 2. S dx x²-x+2

A: Given problem:-

Q: Suppose the semicircle shown to the right is revolved about the x-axis to generate a sphere. Let AB…

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Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫ ln(x-ln(x-.....) dx in terms of some new variable t

Q: Express the integrand as a sum of partial fractions and evaluate the integrals. x+9 S: -dx 2x³ - 8x

A: To express the integrand as a sum of partial fractions and to evaluate the integrals.∫x+92x3-8x dx

Q: 4 2 dx 5₂ is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if x√√x²-4 c→ 2+ Add…

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Q: Solve: 123 1 224 + 1 315 - 4x6 +...? +

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Q: Q3: Show that b. I — = ƒ‰e¯¹8(2t − 2). dt = ½-½ 2e C. L²u(t)dt = = [cosnt. 8(t − 2) + 38(t+1) +…

A: We have to prove the given statement.     According to our guidelines we can solve only three…

Q: 2 y = 3x³+=+6x X

A: We use the formula as given below:

Q: Assume that the given figure is the graph of f'. y in

A: Local Maximum:It is a point within an interval at which function has maximum Value. Local Minimum:It…

Q: If z=x2sinh 4 then 02z дхду

A: Explanation of the answer is as follows

Q: Which of the following is not true about the curve * x² 2 y = (x-2)(x-1) The vertical asymptotes are…

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Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

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Q: SUBJECT: DIFFERENTIAL CALCULUS NOTE: Make the solution detailed and clear in a sheet of paper. 1.…

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Q: 12. Why does working with a special linear system (i.e. an n by n linear system of equations whose…

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Q: 4. Sketch the graph of one function f(x) that has all of the following properties: a.) The domain of…

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Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=&lt;a,b,c&gt; and B=&lt;d,e,f&gt;.

Q: f2₁ (4x + 5) dx

A: ∫-12 4x+5dx

Q: 7* +(7)*. 2 7. If А. 2 О А О в О с O D = 1 then x= В. 4 С. -1 D. 0

A: We will find the value of x in the following step.

Q: IF y = u* + 3u² & u = 3x Find dy dX

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Q: Find the lengths of the curves in Exercises 1-2. If you have a grapher, you may want to graph these…

A: Concept:  For y = f(x) in the Cartesian coordinates defined on interval a,b  The curve length is…

Q: 3. (x² - y²) dx + xy dy = 0

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Q: The equation N (t) = 500 = models the number of people in a town who have heard a rumor 1+49e-0.7t…

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Q: Acceleration due to gravity in feet per squared second is the constant function a(t) = -32. Suppose…

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Q: Approximate the value of In (1000!)

A: Here we have given ln1000!. Now finding it's value we get : As we know that expansion of lnx is…

Q: Consider the differential equation 2xy" - 3y + 3y +³/4 = 0 (1) It turns out that y₁ = r is a…

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Q: Determine the surface area of the swimming pool. Given that the water in the pool has a uniform…

A: There are 4 edges of the swimming pool, given as: 1. x-axis 2. y-axis 3. Curve A y=-0.2x2+3x-6.25 4.…

Q: Compute for f '(3) using the limit definition of derivative if f(x) - 6x²

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