i. Find the area enclosed by the x-axis and the curve x = 1 + e¯², y = t² for x = [1, 2].

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A: First, we know that the volume of the box is given by V=x²h, where x is the length of one side of…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1 + 5y², 1 ≤…

A: If you have any questions let me know in comment box thankyou.

Q: Let y(x)=3 Estimate the slope of the tangent line of y(x) at the point x = 2: nonzero numbers after…

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Q: Find the x and y coordinates of all inflection points. f(x)=x³ +45x2

A: given function

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Q: Use the shortcut rules to mentally calculate the derivative of the given function. f(x) = 2x-1…

A: Step 1: Step 2: Step 3: Step 4:

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A: Given values:ho = 7 ft.u = 70 ft./s Solution:We know, highest distance travelled from initial height…

Q: Polar formulas 4. Assume r = f(), with on [a, ẞ]. Write the following formulas. AREA ARC LENGTH

A: Step 1: Step 2: Step 3: Step 4:

Q: R 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9 ≤ x² + y² ≤ 25 by…

A: The objective of this question is to evaluate the double integral of the function (x² + y²) over a…

Q: 7. Given: sin(x)= ½, sin(y)= ½ and 0<x,y< π <? find the value of the following 2 expression:…

A: Step 1: Step 2: Step 3:

Q: Need help with this one (Thank you!!)

A: Step 1: R.H.S.…

Q: Assume that the cost, in thousands of dollars, of airing x television commercials during a sports…

A: a.) Marginal cost function is the first derivative of the given cost function. Then,     Cost: C(x)…

Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

A: The objective of this question is to find the intervals of concavity and the inflection points of…

Q: Consider the unit vector as shown. Point A is located at the origin. Point E is (1,0,0), Point Fis…

A: Step 1:     Step 2: Step 3: Step 4:

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Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor serie f(x) =…

A: By using the definition of Taylor series to find the first three nonzero termsof the Taylor series.

Q: Complete the given table. (Enter the logarithm function in the form log(b).) Exponential Form 45 =…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (7+2) y = √1+ex,…

A: Step 1:​Given a function here:y=1+ex​,To find: The exact area of the surface obtained by rotating…

Q: A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:

A: cartesian equation is y=7−631x​Explanation:Step 1:given that r=6sinθ+31cosθ42​using cross…

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Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C…

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Q: Josefina is a lifeguard and spots a drowning child 60 meters along the shore and 70 meters from the…

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A: Step 1:To solve the given differential equation:dtdb​+mb(t)=mWe can use the separation of variable…

Q: [Select] of f is a point (c, f(c)) · graph of f where the concavity changes.

A: The objective of the question is to identify the correct term for a point on the graph of a function…

Q: 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9≤ x²+ y² ≤25 by converting…

A: To evaluate the double integral  over the region by converting to polar coordinates.

Q: Find all the second order partial derivatives of the given function. 6) f(x, y) = x² + y = ex+y -

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Q: Show all proper work this is the curve sketching unit in calculus Both a,b,c are part of 1 question

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Q: Section 1: K/U Multiple Choice: [3 Marks] 1. Derivative of y = 14 is: a) 0 b) 1 2. Derivative of…

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Q: Please answer parts a and b

A: The objective of the question is to determine the truthfulness of two statements related to the…

Q: (3) Find all critical points of f(x,y) = -x³+3x+13-31² and classify each as yielding local max.,…

A: Critical points: (-1,0),(-1,2),(1,0),(1,2)Saddle points: (-1,0),(1,2)Relative maximum:(1,0)Relative…

Q: The unemployment rates in a certain region for the years 1994-2014 are shown in the graph. Find the…

A: We are given the graph and we need to find out the average change for the given years.

Q: [1] dx (25+x²) 2 hint: use trigonometric substitution

A: Step 1:

Q: Consider the following. u = (2,-1), v = (4, 1) (a) Find u . v. U⚫v= (b) Find the angle between u and…

A: Step 1: Given vectors are;u= &lt;2,−1&gt; and &lt;4,1&gt;∴u=2i^−j^​ and v=4i^+j^​ Step 2:…

Q: For the vectors p = [1,-2,3], q=[2,1,3], and r=[1,1,0], determine if the following is true: (p x q)…

A: Step 1: Not true  Step 2: Step 3: Step 4:

Q: Q Let x)=x+2x-8. For what value(s) of x does f(x) have a local minimum? Paragraph V B I UA Ev Ev

A: The objective of this question is to find the value of x at which the function f(x) = x^2 + 2x - 8…

Q: 4  For the function shown in the​ graph, give the​ interval(s) where the rate of change of​ f(x)…

A: Step 1:a) The rate of change is positive on the interval where the slope is increasing. From the…

Q: if u=[2,3,0] and v=[0,2,4], find a vector of magnitude 4 perpendicular to u and v

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Q: show all steps please! thank you!

A: The slope of the tangent line at point (x,y) is given as

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Q: solve the non-homogenous equation y” – 2y’ = t + e^t

A: The given equation is a non-homogeneous second order differential equation. The general solution of…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3,    0 ≤…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Let lim f(x) = 17 and lim g(x) = 11. Use the limit rules to find the limit below. x-9 x+9 lim…

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Q: Find the slope of the tangent line to the polar curve r=4-5cos(theta) at theta = pi/3

A: If you have any questions let me know in comment box thankyou for your question.

Q: Find the average rate of change for the following function. 2 f(x)=5x³-3x² + 2 between x = -2 and x…

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