I did the first number. Answer only number 2 and 3. Evaluate the following limits.

Q: Consider the following function. (x) = x5 + 4x³) Find f'(x). f'(x) = Does f have an inverse function...

A: Given that f(x) = 1/8 (x5 +4x3)

Q: 1- cos?t lim t-0 t

A:

Q: b) Show that y = 2sin (2x) is a solution to the differential equation: - 64 =0

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: We know that for the vector u = ai + bj + ck, the unit vector is  u^ = aa2+b2+c2i + ba2+b2+c2j + ca2...

Q: dy 3 1. a) Solve the differential equation dx if y = 3 when x = 1. xy

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y =x' and x = y about the x-...

A: Given query is to find the volume of solid generated.

Q: x -4 ifx<2 Determine f(2) if f(x)= {2-x if 2 <x<4. x-2 if 4 <x

A: Given,           fx=x2-4if x≤22-xif 2&lt;x≤4x-2if 4&lt;xTo find : Determine f'+2.

Q: Evaluate the fo llowing limits lim x8 + 7x + 9x-4x² +2 Xヨ-0 x4 - 4 y5 - 3x*-6x +4 2x2-8x +7 suppose ...

A: 1) To evaluate:  limx→-∞x8+7x6+9x5-4x2+2x4-4x5-3x2-6x+4 Dividing numerator and denominator by x4, we...

Q: y? = 8x, y = 2x; about y = 4.

A: Given that y2=8x,y=2x about y=4 . Here we have to find the volume of the solid generated by revolvin...

Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 s y s 2, y – 1sx s 1} 328 3.

A:

Q: Use implicit differentiation to find y". y2 - x² = 6

A:

Q: Find the coordinates of a point on a circle with radius 20 corresponding to an angle of 175 degrees

A: Given query is to find the coordinates of the point.

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1....

A:

Q: nd the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form ...

A:

Q: dx T² + 4 2

A: We have to find value of indefinite Integration.

Q: The diagonal of a cube can be derived by Pythagorean Theorem using the diagonal of a square and the ...

A:

Q: Prove that lim (4x2 – 25) = -9 x-2

A:

Q: 6y - 24y +x = 0, x= 0 %3D

A: answer of given question is in step 2

Q: tion 4x + 200 A garden shop determines the demand function q = D(x) = during early summer for tomato...

A:

Q: X - 5 dx -2x + 2

A:

Q: dw 21. : 1-cosw A. -tan w + secw + C B. w – cotw + C C.-cotw – cscw + C_ D. -cscw + tanw + C

A: We can find the integral value as below.

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: Since the start of July, OHaganBooks.com has seen its weekly sales increase. OHaganBooks.com fits th...

A: Let's find. 

Q: The sequence that begins 3, 3, 6, 9, 15, 24, ... could be O a geometric sequence. a Fibonacci sequen...

A: Topic = Sequence This Sequence could be a Fibonacci sequence.

Q: The rose r = asin 30

A: Solution is given below:

Q: 3. Determine whether the series below converges or diverges using the test that you think is easy! 2...

A: Solved below

Q: 2. Given: LKEI S LTEI Prove: AKET ATEI Proof: Statements Reasons 1. 1. 2. 2. 3. 3. El EI 4. 4.

A:

Q: (a) Find the differential dy of y = e#/5. (b) Evaluate dy for a = 0, dx = .1. (a) dy = dx (b) dy =

A: Solved below

Q: Find f x) and f xof fCx) = 11x³

A:

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A: topic - vectors 

Q: Use a linear approximation (or differentials) to estimate the given number. (8.09)2/3

A:

Q: 0 < 0 < In 3 1.arc length of a spiral: = 20 , where %3D

A:

Q: Use the limit definition in finding/showing what is asked. 1. Find an equation of the line tangent t...

A:

Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x3 ...

A:

Q: Find the length of the tangent to a circle from point of tangency to point (8,2) . The circle is def...

A:

Q: x®+7x6+9x5-4x²+2 lim x--00 x6-4x5-3x2-6x+4

A:

Q: DO NOT include the variable in your answer. Given the graph off'(x) below, what is the slope of the ...

A:

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A: Vectors with opposite directions have 180° angle between them.x and y components have opposite signs...

Q: Solve the following initial value problem. y6) -2y" +y' 3 + 7x e*; y(0)=y'(0) = 0, y"(0)= 1 The solu...

A:

Q: Determine where the function is (a) increasing: (b) decreasing, and (c) detormine where relative ext...

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) sin3 50 v cos 50 de

A:

Q: Write an equivalent first-order differential equation and initial condition for y. y = 2- |(5+ y(t))...

A: Find your answer below 

Q: Find the following antiderivatives. a. ∫(3x^4-cosx)dx b. ∫(5^3sqrt(x^2) + 2x-1)dx c. ∫((1/x^3)+5)...

A: ∫xn dx = xn+1n+1+C. ∫ax dx = axloga+C

Q: y = 100(1 – e-0.451t). (a) What function gives the instantaneous rate of change of the concentration...

A: Given query is to find the rate of chnage for the function.

Q: dt 20.5 t2+2t A - In|t? + 2t| + C B. 2ln +C C. In +C D. In + C

A: First we common out t2 from denominator and then put 1+2/t=u and differentiate both sides with respe...

Q: 1. Calculate the area enclosed by the line y 2x + 3, the x-axis, and the lines x 1 and x- 3.

A:

Q: Find the volume of the solid enclosed by the paraboloid z = 4 + x2 + (y – 2)2 and the planes z = 1, ...

A:

Q: Find the exact value of the expression. cos(160°) cos(25°) + sin(160°) sin(25°)

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Q: Evaluate the limits analytically sin rte –1 A. lim,-→0 I COS I

A: Find your answer below