1. Find the derivatives of the following functions: a) f(x) = 2x³ + e²x b) f(x) = ln (2x - 1)5

Q: Remove arbitrary constant in the given relation. x = sin (w t + ß); w - parameter, not to be removed

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Q: Find the slope of the tangent line to the parametric curve x = 4 cos(t), y = 3 sin(t) when t= π/2.

A: We have to find slope of tangent line at given 't' value. Topic :- Application of derivative.

Q: Consider the following. e-10x = 2 (a) Find the exact solution of the exponential equation in terms…

A: As we know that lnem=m lne=m  as lne=1

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Q: Solve the equation. (Enter your answers as a comma-separated list. If an answer does not exist,…

A: Given query is to find the value of x.

Q: 6. Find the polar coordinates if (x, y) = (-√3, 1), r≥ 0, -2π <0 ≤0 (a) (2,117) (2,117) (b) (d)…

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Q: Find an equation that has solutions x = 2 and x = - 2 both of multiplicity 2. Write your answer in…

A: Given query is to find indicated function.

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A: Given14e-4t = 0.9

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A: GivenF=sin(4x+2z)i-6yexzkWe are required to finddiv(F)curl(F)

Q: coterminal

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Q: Integral Calculus (Upvote will be given. Please write the complete solutions with GRAPH/DIAGRAM…

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Q: Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 20L0.75 K-0.25 where…

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Q: 12 2 √x - 3 ах

A: ∫3122x-3dx

Q: 9. lim 818 4x + 3 5x − 1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: FIND THI (GEOMETRIC APPLICATIONS) Find the orthogonal trajectory of the given family of anver 3 1.)…

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Q: Integrate. 4 /(-5e²+) de = 7 dx ? Choose 1 answer: A -5+ In 4 +C -5+4 ln x + C O-5e + In 4 + C O-5e…

A: Given query is to find the integral.

Q: spherical balloon is being deflated so that its radius is decreasing at a te of 2 cm/min. How…

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Q: Pictured is the graph of y=f(x). I need help transforming it to y=1/2f(x). Can someone explain?…

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Q: (part Determine two coterminal angles (one posi- tive and one negative) for a)-400° 1.313 and -47…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

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Q: The Divergence Test for infinite series (also called the "n-th term test for divergence of a…

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Q: Determine the values of λ for which the system below has nontrivial solutions. (5-2)x-5y=0…

A: The given equations are; (5-lamda)x-5y=0 -3x+(3-lamda)y=0

Q: A ball is thrown vertically up from the ground. If the positive direction is upward, then h = -16t²…

A: Answer is in step 2.

Q: Suppose that the cost (in dollars) for a company to produce a pairs of a new line of jeans is C(x) =…

A: Let's find marginal cost. Cost function is given.

Q: Find the nth Taylor polynomial centered at c. f(x) = In(x), n = 4, c = 4 P4(x)

A: We have to find the nth Taylor polynomial centered at c  f(x) = ln(x), n = 4, c = 4

Q: (b) F(t)=(e²¹)i + (2e²¹ +5)j + (2e²¹ -20)k for 0≤1≤ In 2

A: As we know that: The expression for the length of vector-valued curve in the interval a≤t≤b is:…

Q: Graph f(x)=sin(x) + 1 in Desmos. Make sure you graph using radians and use the window where -2m ≤ ≤…

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Q: m to be removed -

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Q: Find the first partial derivatives of the function f(x, y) = ln (x + √√x² + y² 1. fx(3, 4) = 2.…

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Q: Let and Compute B - A. e O b) O O 4 -5 -3 5 -9 7 -4 5 3 -5 9 -7 6 5 7 3 1 3 d) Not possible. 9 -5 -1…

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Q: Solve the system of linear equations using the inverse matrix O C S S 80 x - 2y - 4z = 2 2x-3y-6z =…

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Q: (a) Use the information you answered on number 10 to graph the function from that problem. 10) P(x)…

A: (a) The polynomial to be plotted is Px=x4+3x3-3x2-7x+6. The factorization of the polynomial can be…

Q: Solve the equation. (Enter your answers as a comma-separated list. If an answer does not exist,…

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Q: a. 4x² + 12x + 4y² + 16y - 11 = 0 b. x² + y²-6x + 4y +4 = 0 c. x² + y²-4x-8y + 20 = 0

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Q: Find the distance between (1,5) and (1,1).

A: We have to find the distance between the points 1,π2 and 1,π

Q: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: The given data is: If the trough is being filled with water at the rate of 0.1 m3/min dVdt=0.1m3/min…

Q: 3. 00 Find the radius of convergence for Σ (5x) k=1 (a) (c) 5 1|5 (b) 1 (d) 0

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Q: -4-x² - y² 4 component. For the function f(x, y) (-3, -3) that has a positive find a unit tangent…

A: Let's find unit tangent vector.

Q: Integral Calculus - Plane Area Find the area of the region between x=y2-1 and x=y+1 using a…

A: Givenn functions:- x=y2-1, x=y+1

Q: 2 كل ك 0.5 , 3- = (f(x رشد -

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Q: 32. √ ₁²+2x-3d²

A: Given integral I=∫xx2+2x-3 dx

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A: The given region is:x=33y ,      x=0    and     y=2

Q: Remove arbitrary constant in the given relation. y = C1 + C₂ e -4x

A: The given function, y=c1+c2e-4x We have to eliminate the arbitrary constants.

Q: Suppose f(x) = 3x + 4. Then the inverse of fis given by ƒ-¹(x) = Moreover, ƒ'(x) = ₁ and (ƒ−¹)'(x)…

A: we need to find out the inverse of the function.

Q: 1. Use the limit comparison test to determine whether the infinite series is conver a. Σn=27³-1 b.…

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Q: A constant volume of cookie dough is formed into a cylinder with a relatively small height and large…

A: We know  Volume of cylinder=πr2h r=radius of cylinder h=height of cylinder

Q: Differentiate y = arctan(2). y' =

A: Given: y=arctanx   As we know that: The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And use…

Q: Find the second partial derivatives of the function f(x, y) = x³y³ + 2x³y. 02f მ2 1. 2. 3. 4. - მ2f…

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Q: 4 3 2 1 04 -1 -2 -3 -4 -5 -6 -7 -8 -1 V 0 2 3 4 Velocity vs. Time 1 t 5 6 he velocity graph…

A: To solve the problem from the corresponding graph.

Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 2x² + 4y² = 24

A: To find the maximum and minimum values of the function fx, y=x2y subject to 2x2+4y2=24.