Find the critical numbers and any local maximum and minimum points for the function ex f(x) = 2x Find exact values.

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) (x(t), y(t),…

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Q: Find the general solution of the differential equation y" — 4y' + 104y = 0. NOTE: Use c₁ and ce as…

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Q: 1(3). If f(x) = 2 cos x + x³, find 06 2 4 8

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Q: A particle is moving along the x-axis so that its velocity at any time t≥ 0 is given by v(t) = 5tet…

A: Explanation of the answer is as follows

Q: Sketch the graph of f and use your sketch to find the absolute and lo f(x) = sin(x), 2 absolute…

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Q: 19 Can a graph with three vertices of degrees 2, 1, 4 exist? Yes No

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Q: y = 2 sin(x), y = ex, x = 0, X = K|N 2

A: The region bounded by the curves,  y=2 sin(x), y=ex, x=0, x=π2

Q: A graph consisting only of a vertex is a complete graph. True False

A: Recall:  The complete graph on zero/one nodes is a trivial graph also known as the null…

Q: Find an equation of the hyperbola that has foci at (0, -15) and (0, 15), and asymptotes y= 3 3 2x…

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Q: Evaluate: S (5 — 2 sec 0 tan 0) de - O 0.79 0.68 O 0.95 0.84

A: ∫π6π4(5-2secθtanθ)dθ

Q: Find y': ○ 4kx (2kx + 1)7 ○ 4k (2kx + 1)7 ○ 8k(kx² + 1)7 ○ 8kx(kx² + 1)7 y = 1/(kx² + 1)8 ; k…

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Q: Evaluate: xe² dx Ső 0e-2 0e² 1 - 0/(e-1) 22

A: Evaluate the integral

Q: Given : y = cot √2x + 1 Find dy dx O csc² √2x + 1 √2x+1 O csc² √2x + 1 2√2x+1

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Q: Fill in the blanks: 2² + 1 The equation describes an ellipse. The volume of the solid obtained by…

A: We need to find volume.

Q: Use the Inverse Function Theorem to find (p-¹) (2) given that p(x) = √√x - 7. Note that p(−11) = 2.…

A: The solution is given below

Q: Find the general solutions of the system. 7-9 0 x' = + 1 13 0 x 1 3 10 x(t) =

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: At point (1,-1,2). 4

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Q: 11. What point on the curve y = x4, does the normal have a slope of 16

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Q: The plot below represents the function f(x) 8+ 7 4 5 6 5 4 3 2 1 -5 -4 -3 -2 -1 -1 1-24 Evaluate…

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Q: I Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A: Given that Line is passes through A(1,2,3) and B(5,1,7) And plane passes through C(1,0,2) D(5,1,6)…

Q: ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated…

A: You have asked question (2) According to question,Given Matrix,A = 3006-306-63Eigen Values = 3, -3

Q: dx 5 - 2x Evaluate: S O2 ln |5-2x + C -2 + C 5-2x O -1 2(5-2x) + C On 15 - 2x + C

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Q: Find dy given that x = sec² y y. dx Osec² ytan y cos² y tan y 2 Osin² y cot y O cos² y cot y

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Q: Find the volume of the region that lies below the parabola y2 = x and above the x-axis the interval…

A: Given curves is y2=x

Q: I(X) {(-2,1), (1,4), (2,5), (3,6) g(x) = 6 + 4x h(x) = -x² + 2 2. 2h(3)+g[f(-2)] find 1. h[f(1)] 7…

A: 1. hf17=h47                  =-16+27                   =-147                    =-22.…

Q: Find the producers' surplus at a price level of p = $56 for the price-supply equation below. p=…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) [(7x² + 8 + 2²1) dx +

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Q: f(x-1) e-2x+x² dx = O 1 -2x+x² e 2 2e-2+2x+C 2e-²x+x² + C e-2x+x² + C + C

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Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

Q: In the attached figure are represented the continuous functions g: R → R and h: R → R 9 h If it is…

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Q: 2. Evaluate 6x²e4x³ dx.

A: Let 4x3 = t

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

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Q: Cos de 1-Sin e

A: To evaluate: I=∫cos3θ1-sin θdθ=∫cos2θ×cos θ1-sin θdθ=∫(1-sin2θ)cos θ1-sin θdθ=∫(1-sin θ)(1+sin θ)cos…

Q: Find the average value f of the function f on the given interval. ave f(x) = 6x - x², [0, 2]

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Q: Evaluate the integral. (Use C for the constant of integration.) tan³(x) sec(x) dx

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Q: B)Prove (cose + i sine)" = cosne + i sin no

A: Solution is given below:

Q: 10. The function g(x) = x² − kx³ − 9x² + 7x − 8 has a minimum when x value of k. = 3. Determine the

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Q: Consider the following sequence x₁ = √₁, x₂ = √1 + √I, x3 = √1+√₁+√₁ Evaluate lim xn (No credit for…

A: The given sequence,x1=1, x2=1+1, x3=1+1+1

Q: 14) A 300-foot cable weighting 4 pounds per is hanging from which 300 feet Level. Find ground the…

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Q: Find the general solution of the following differential equation. y" - 11y' + 18y = 0 NOTE: Use c₁…

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Q: sin20 B)Evaluate the integrals: i) f/20 rdrde ii) f/2/2fix z² siny dz dy dx. sinx tt)

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Q: If [ f(x) dx O 10 0 2 O O -2 = 4 and 4 [*g(x)dx = 6, what is 5 2 [ f(x)dx + ² g(x)dx? 4

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Q: Integrate the following: 1. fxsinxdx 2. fæcos2xdx 3. fe sinxdx

A: The given integrals are' 1) xsinx 2)xcos2x 3)exsinx.  Repost the next parts.

Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: Determine where the function discontinuous. [-(x+2)² +1→x≤-2 f(x)=x+1→-2≤x≤3 [(x-3)² −1→x>3 Using…

A: the given function,  f(x)=-x+22+1,x≤-2x+1,-2≤x≤3x-32-1,x>3

Q: Find and sketch the domain of the function. f(x, y) = √√√√4x²-√√25-y² O -6 DO -4 -6F 4 6 -6 -4 4 4…

A: The set of points (x, y) where the function f(x, y) is called the domain of f(x,y).

Q: Find the equation of the tangent to the function y = cos(2x) at the point where x = л/4.

A: equation of a tangent line

Q: Cos y dy 1-siny

A: The given integral is: I=∫cos2y1-sinydy   As we know that; The trigonometric identity: sin2x+cos2x=1…

Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y(x) is the solution of the…

A: To solve the initial value problem.