If In a = 2, ln b = 3, and ln c = 5, evaluate the following: a² b²c4 (a) In = (b) In √a²b²c4 =

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Q: h X f! 1-X.

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Q: Find the critical numbers for h(x)=x^2-x^4. Show all work.

A: The objective of the question is determine all the critical point of the given function.

Q: 3. A science project studying catapults sent a projectile into the air with an initial velocity of…

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Q: Evaluate using integration by parts: fx sec-¹x dx

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Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) = c₁cos(x) +…

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Q: 9w k=1 k² +2k*r 8k² +1 A. By the properties of 1. geometric series 2. p-Series 3. Divergence Test 4.…

A: Divergence Test: If limk→∞ak ≠ 0 then ∑k=1∞ak diverges.

Q: 1) Solve the following ODES by Undetermined Coeff. ● 4X 11 X y - 16 y = 19.2 € + 60e, y(a) = y() -4X…

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Q: Find an angle coterminal to  25π/3 that is between 0 and 2π

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Q: 3 12 Find the exact value of sin (a + B), if sin a= and sin ß= 5 13' sin (a+B) = ? OA. -16 65 OE. 33…

A: Given that sin α=35 and sin β=1213, with α and β in quadrant I

Q: Consider the following differential equation to be solved by variation of parameters. y" + y =…

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Q: Solve the differential equation by variation of parameters. y" + y = csc(x)

A: Our Aim is to solve the differential equation given below using variation of parameters.y"+y= csc…

Q: Suppose that $600 are deposited at the beginning of each quarter for 10 years into an account that…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: Evaluate the following limit or explain why it does not exist. 6 X lim (1+7x) X-0 Select the correct…

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Q: Suppose that the graph below is the graph of f '(x), the derivative of f(x). Find the open intervals…

A: To find the inflection point.

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (3, 2, 5)…

A: Since you have posted multiple questions. As per guidelines we"ll solve only  first question. If you…

Q: [² (8cx² = 6cx+6c) de Identify the variable of integration in the given definite integral. Type only…

A: Given problem:- ∫pq8cx2-6cx+6cdc

Q: 10. (a) Construct the Taylor polynomial p3(x) of degree 3 for the function f(x) = 1/(2-x) around x =…

A: Solution is given below:

Q: -3 Evaluate the integral ſ² ſ² ſ²₁ xz(y + 1)dxdydz

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Q: 69. Tangent Line Find an equation of the line tangent to the circle x² + y² = 169 at the point (5,…

A: The tangent line to the circle x2+y2=169 at the point 5,12

Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 16y = 12x + 6 y(x) =

A: The given differential equation is;  y''-8y'+16y=12x+6.

Q: Find the absolute maximum and minimum values of the following function on the given region R.…

A: To find the absolute maximum and minimum.

Q: MHF4U Name: Date 3. Erin travels north and south from Main Station. The distance, in km, of the…

A: We need to find time.

Q: Find the derivative of f(x) = (2x+1)³(3x - 1)³. Show all your work and factor the result completely

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Q: 2 (D" +8D² +16) y = - sinx Ans: y=as2x+ C₂ Sin2x + C3 XC052 X + (4x sin2x-sinx

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Q: g(b)= g'(b)= Calculate g(b) and g'(b) where g(x) is the inverse of f(x) - 18, where b=4 248

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Q: ct rit Find the x-value of all points where the function below has any relative extrema. Find the…

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Q: 3. A white wine at room temperature 70° F is chilled in ice (32°F). If it takes 15 minutes for the…

A: The solution is given below

Q: Evaluate the following expressions. Your answer must be an exact angle in radians and in the…

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Q: Use CRAMER'S RULE to solve the system : 2x-y-z = 2 4x + y -z =-5 6x - 2y +2z=17

A: To solve the system using Cramer's rule.

Q: Solve the problem. 16) The graph shows the height h (in meters) of a roller coaster t seconds after…

A: In this question, we need to find the time intervals in which the height of roller caster is…

Q: The derivative of a function of fat z is given by provided the limit exists. f(x+h)-f(x) = f'(x) =…

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Q: When Newton's Method is used to approximate the root of f(x) = x³ + 2x² - 1 in in the interval [0,…

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Q: x, evaluate each expression.

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Q: he base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x². Cross…

A: To find the volume.

Q: Average Cost Jesaki Water Sports incurs the following costs in producing a water ski vests in one…

A: Here we have to use the concept of derivatives

Q: x = est, y = to (a) Find dw/dt by using the appropriate Chain Rule. dw dt W = X- (b) Find dw/dt by…

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Q: Determine the remaining sides and angles of the triangle ABC. What is the measure of angle B? 0° B…

A: This is a problem related to sine cosine rule of trigonometry. Please follow the procedure given…

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Q: 2 y = (x ² + 1)² Find dy dx

A: To find derivative.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: A circular plate is submerged in a water of weight density (pg) 9810 N/m³. If the total force on the…

A: the answer is given in step2

Q: 3. Evaluate SIS 3z dV where E is the region inside both x² + y² + z² = 1 and z = E x² + y².

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Q: Do question 33.

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Q: lim x→5 3x |x-5|

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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