6. Calculate the locations of maximums and minimums of the following functions: Show work in details. f(x) = x³ – 3x +2 f(x) = x' – 82² +3 %3D

Q: To find two real numbers whose difference i and whose product is minimum, we can find minimum value…

A: Topic:- calculus

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Solve the following

Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: Determine the antiderivatives of the following functions: 1. V36-x² dx 2. J 9x2+36dx 1 S- x In…

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Q: , can you draw the graphs clearer? or maybe in digital?

A: Given problem:- Draw the figure which represents area bounded by given curves 1) y= x2+2 , x=2 and…

Q: A power representation of the function f(r) = for -1 <a<1 is 1+ %3D

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Q: Consider the function f(x) = The value of f'(0) is: (x+ 1)2

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Q: Using the fundamental theorem of calculus, find the area of the regions bounded by y= 5-x^2 and the…

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Q: 5. Let f(x) be the function f(x) = {* T*7 makes the function f(x) continuous for all real numbers.…

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Q: Use implicit differentiation to find the point in the first quadrant on the ellipse 8x2 + 4y? slope…

A: Question- Use implicit differentiation to find the point in the first quadrant on the ellipse 8x² +…

Q: y=v16-x 2.

A: This question is based on application of integration.

Q: Calculate the area of the region limited by the equation r = 2+2cos φ

A: Given:  r = 2+2cos φ.

Q: Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9)

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Q: Find the following for the vectors u = 6i + 3j + /2k and v = - 6i – 3j – /2k. a. v•u, Įv], and Ju|…

A: We will solve the problem on vector dot product and projection.

Q: 1. Consider A = (0,4, 2), B = (6,0,0) and C = (3,0,-1). %3D %3D (a) Find the unit vector in the same…

A: B-2A+C=&lt;6,0,0&gt;-2&lt;0,4,2&gt;+&lt;3,0,-1&gt;…

Q: 7. Let f(x) = -3x + 9x - 3. a. Determine the x values where f"(x) = 0. b. Fill in the table below to…

A: In this question we have to find first three subpart.

Q: 3) y"+2y'-8y 0, y(0) = 1, y'(0) = 8.

A: Given:y''+2y'-8y=0y(0)=1 y'(0)=8

Q: 27. f(1) = 1 + e*i 28. f(1) = r² - e- + 5 29. f(1) = (1 + e²)2 30. f(1) = (e' – e¯)? 31. f(1) = 41²…

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Q: Determine the equation of the tangent line to the curve, y = 4x e at x = 1. Use exact values.

A: Given y=e4xx3     at x=1To find equation of tangent:

Q: 2. Determine a•5 for each of the following a) å = (7, -3,5)andb = (-5,11, -2) 3. Determine the angle…

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Q: dy Find dx y = = 5x° sin x coS X

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Q: Evaluate the limit In(x) lim x+1 x2 - 19x+ 18 a. 1 19 O b. 19 C. 1 17 O d. None of these. е. —17

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Q: In n Consider the series Verify that the hypotheses of the Integral Test hold, and n2 n=1 use the…

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Q: Find the solution of the differential equation dy x+y=x²y² dx

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Q: For an arithmetic sequence, a17 = 2. If the common difference is 5, find: aj = the sum of the first…

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Q: dx (9 – 4.x²)³/2 2,3/2

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Q: Determine a.5 tor each of the following i = (7, -3.5)andb = (-5,11. -2) b) a = (-15.13), 5 = (14,…

A: If a→ = a1 , a2 , … , an and b→ = b1 , b2 , … , bn then  a→·b→ = a1b1 + a2b2 + … + anbn

Q: Given the graphi of the function f(x) below, answer the following 37 26 8 16 -10- 20- Enter T for…

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Q: Evaluate the following integrals: 1. S(cos x + csc² x)dx 2. S(tan x + sec² x)dx 3. S(1+sec²x)dx 4.…

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Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

A:

Q: X-1 4 = = 2 – y = z 2 y-2 z-1 12 = x = -1, 3 2 Show that these are skew lines.

A: To show that the given lines are skew lines.

Q: QV Determine whether the given differential equations are bomogenous and, if so, solve them. a) xydy…

A: To find out that the given differential equations are homogeneous or not.  According to company…

Q: der the series. You will apply a comparison test to determine the sin n=1 3 behavior. Do the…

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Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

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Q: 3. A girl is flying a kite on a string. The kite is 120 ft. above the ground and the wind is blowing…

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Q: mine the value(s) of x where the slope of the tangent line is horizontal. Use exact valı…

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Q: 1. Consider the lines x = -1+ 2s by:- = and t2: y=s x – 5 l1 : 3 – z %3D 4 z = 5+ s а. Find two unit…

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Q: P(x) = 23x – a?. %3D

A:

Q: 2. Find the volume of the solid bounded by z = 0, x = y2,z= 3, x = 4 - y2. (graph the solid)

A: Given problem:- Find the volume of the solid bounded by z = 0, x = y2 ,z= 3, x = 4 - y2

Q: 3 Σ n(n + 1) n= 1 The first partial sum is S, = (Type an integer or decimal rounded to four decimal…

A:

Q: An object’s position function, s, in meters, is given by s(t)= -4.9t 2 +13.2t, where t is measured…

A:

Q: scientific

A: We will find the 28th term

Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

A:

Q: 6. Calculate the locations of maximums and minimums of the following functions: Show work in…

A:

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

A: Parametric equation of line passing through a point x0,y0,z0 in the direction of N=a,b,c is…

Q: pints A and B are separated by a lake. To find the distance between them, a surveyor locates a point…

A: Given query is to find the distance AB.

Q: Evaluate the integral [(4?) i + (3) j+ (5t + 3) k] dt. 1 i + (3) j+ (5t + 3) k] dt = (O i+ O ij+ (O.…

A: Topic = Integration

Q: 7. Find the volume of the solid obtained by rotating the region bounded by and r = 0 about the…

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Q: The limit lim (x In( cos x-00 is an indeterminate form of type 0 0o. Select one: True False

A:

Q: Using the fundamental theorem of calculus, find the area of the regions bounded by y=8-x, x=0, x=6,…

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