SOLVE THE FOLLOWING 14. = In (x² + 1) 15. = In (Inu)

Q: Find the directional derivative of f(x, y, z) = xy + z at the point P = (2, –6, –-1) in the directio...

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Q: The top and bottom margins of a poster_are 6 cm and the side margins are 4 cm. If the area of the pr...

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Q: Express the following series as a telescoping sum and evaluate its nth partial sum. 2n+1 06. E (Hint...

A: We can solve as follows

Q: r(x)=1/2x   Step 2 of 2 :  Find two points on the graph of this function, other than the origin, t...

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Q: y" – 2y' + y = -3 – x + x², y(0) = –2, y'(0) = 1. %3D %3D

A: Given: y''-2y'+y=-3-x+x2 ; y0=-2, y'0=1 So, We can also write as; D2-2D+1y=-3-x+x2   The auxiliary e...

Q: by implicit differentiation. dx Find 3xeY + ye = 4

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Q: Question 1 xi+yj+zk If F(xy,z)- Vx² + y²+z² .2 Determine Vx F

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into ...

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Q: Find the probability for the experiment of tossing a six-sided die twice. The sum is 2,4, or 7.

A: We have to find probability of die rolled twice

Q: TT 1 4.) S“ S,x² sin(xy) dydx

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Q: An irigation system uses a straight sprinkler piper 300 t long that pivots around a central point as...

A: We can find the area as below.

Q: Sketch the region bounded by the given curves and find its centroid

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Q: Find the point P such that v = PQ has the components (4, 3, -10.5). Q = (5,9, -8.5) P =

A: To solve the following vector

Q: Test the series below for convergence using the Ratio Test. 87 n! n=1 The limit of the ratio test si...

A: Given query is to find series converges or diverges.

Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: A population grows according to an exponential growth model. The initial population is P0=4P0=4, and...

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Q: Prove the identity. (Recall sinh(a + b) = sinh(a) cosh(b) + cosh(a) sinh(b).) sinh(2x) = 2 sinh(x) c...

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Q: A person walking along a straight path has her velocity in miles per hour at time t given by the fun...

A: Given: vt=0.25t3-1.5t2+3t+0.25,                     0≤t≤2 v(t) is the velocity in miles per hour. t ...

Q: Directions: Find the limit of the following. 1. lim(x² + 2x – 1) x→2 2. lim (x³ + 8) X--2

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Q: Find the equation of the tangent line to the graph of the given function at the point with the indic...

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Q: Evaluate the following integral using partial fractions: 2x2 +1 dx J(x – 1)(x – 2)(x – 3) -

A: Given: I=∫2x2+1x-1x-2x-3dx   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx ; where a is cons...

Q: For each differential equation in Problems 1–21, find the general solution by finding the homogeneou...

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Q: Find all values of x for which the series converges. (Enter your answer using interval notation n X ...

A: Since multiple questions are asked, I am answering the first question only.

Q: x sec (3x) tan (3x)dx

A: Find your answer below 

Q: what is the domain and range of: f(x) = √x −ln(x).

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Q: If f(x) = 3x2 – 3x – 25, find f'(x). %3D - f'(x) = Find f'(1). f'(1) = %3D

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Q: g(b) Use the substitution formula, f(g(x)) g'(x) dx = | f(u) du where g(x) = u, to evaluate the foll...

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Q: Directions: Find the limit of the following. 4х-5 3. lim X-3 \5x-1 4. lim (sin x)

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Q: A road perpendicular to a highway leads to a farmhouse located 4 mile away. An automobile traveling ...

A: topic - application of derivatives

Q: Consider the following function and express the relationship between a small change in x and the cor...

A: Given f(x)=cot 8x

Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into ...

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Q: x²-2x -3 (15) Rational function r(x) = has a vertical asymptote at x = 4. The asymptotic behavior X-...

A: Solve the following

Q: Find dy/dæ in terms of t if x = te', y = -2t – 2e dy/dx = %3D

A: topic =derivative

Q: A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 cm. by 15 cm. by cu...

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Q: 1 -dx 2 xV 64 + 9x°

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Q: | cos (5x) cos (3x)dx

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Q: Calculate L4 for f(x) = 42 cos () over L4 = %3D

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Q: Help

A: Topic:- simplification

Q: (3, 2) 1- 1 3 4 Graph of g' The graph of g', the first derivative of the function g, consists of a s...

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Q: Vn +1-

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Q: Evaluate the integral. 3* dx V3* + 4

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Q: Eliminate the parameter. x (t) =1– e', y (t) = e2t. State the domain.

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Q: 1 dx 1+ 2 sin? x

A: Integral

Q: (4) Find the domain of f(x) = Vx3 – 2x² – 24x. (A) [-4, 0] (B) (6, ∞) (C) [-4, 0] U [6, ∞) (D) [-4, ...

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Q: x=r' +1, y=r -t d'y b) Find dx?

A: Given: x=t3+1y=t2-t To Find:  To find d2ydx2.  

Q: Give two other polar coordinate representations of the point, one with r 0. (r, 0) = (3, – 2.14 X )...

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Q: Let f(x, y, z) = xy+ z', x = r+ s- 31, y = 3rt, z = s'. Use the Chain Rule to calculate the partial ...

A: Chain Rule: If f=f(x,y,z), x=g(r,s,t), y=h(r,s,t), z=i(r,s,t) then, ∂f∂r=∂f∂x∂x∂r+∂f∂y∂y∂r+∂z∂r

Q: Write the equation of the tangent line to the curve at the given point. 4x2 – 2y2 + 3xy – 3x = 26 at...

A: We can find the equation of tangent line to the curve at the given point in the following steps.

Q: Find the first five terms of the sequence of partial sums. (Round your answers to four decimal place...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: A small island is 6 miles from the nearest point P on the straight shoreline of a large lake. If a w...

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