Given two differentiable functions fand g, the derivative of the function f(x) - g(x) can be evaluated using the chain rule. O True O False For differentiable functions f and g, we have that the derivative of their product is f. g' + f.g. O True False

Q: 7) Write the algebraic representation for the given piecewise function, using function notation. (…

A: When x≤1f(x) is the upward parabola with vertex (0,-2)

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: 7 Calculate (4x + x²) dx, given the following. 40 [(42+x²) 2 √x²dx 2 335 3 8 |-- dx = 7 S(4x + x²)…

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Q: A small house has a kitchen, living room, and bedroom. The kitchen has an area of 234 ft². The…

A: Given:- Area of kitchen =234 ft2 Area of living room =402 ft2 Area of bedroom =220 ft2

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: 778) Solve for A,B,C,...,H in: (5*9i)=A+jB; (81*8i)=C+iD; 18 (4+4i)=E+iF; ans: 8 (5+91) (2+5i)=G+iH.

A: Topic - Complex numbers We are given, (5*9i)=A+jB (8i*8i)=C+iD ;i8(4+4i)=E+iF ;(5+9i)(2+5i)=G+iH and…

Q: Page < 1. The following is the graph of f. Find the following limits. State if the limit does not…

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Q: Find an equation for the given polar graph. NOTE: Numeric label on this graph represents distance…

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Q: Finding the Domain and Range of a Function: f(x)=√x² – 3x + 2. O Domain: all x ±4 Domain: all x ±2…

A: Given :fx=x2-3x+2

Q: An isosceles triangle is inscribed in a semicircle, as shown in the diagram, and it continues to be…

A: An isosceles triangle is inscribed in a semicircle as shown in the diagram, and it continuous to be…

Q: K Use the graphs of f and g to find (f+g)(-2). (f+g)(-2)= gi Q Q

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Q: Cos X- cosy Jax-sinxsiny dy=2

A: A differential equation of the form Mdx+Ndy=0 called exact differential equation if ∂M∂y=∂N∂x and…

Q: (d). ANS: lim an an = sin() n = 1. (Use l'Hôpital's rule to show that limg-00 sin(1/2) 1/2 = 1.) =

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Q: If z = (x + y)e and x = 7t and y = 1- t², find the following derivative using the chain rule. Enter…

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Q: Find an equation of the parabola with vertex (2,-4) and focus (2, -7). 2

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Q: Calculate all four second-order partial derivatives of f(x, y) = 2x²y + 9xy³. fxx (x, y) fxy (x, y)…

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Q: Given the functions below, find the domain of (fog)(x). (2)-22+6 Select the correct answer below All…

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Q: 2. Find dx/dy if y = √√√1+√x -4√√√√1+√T 4√√√1+√I

A: Given: So,      dydx=1+x'        =121+x1+x'        =121+x·12x        =14x1+x

Q: a. Find the equation of the line tangent to the following curve at the given value of x. b. Use a…

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Q: Given the function () below, decompose A(z) into component functions f(x) and g(x) so that A(z) —…

A: We can answer both the question in the below steps.

Q: tan 2x lim 3 X-0 X + a 2 X sin bx X = 0

A: Topic:- calculus

Q: f(−3)=3, f'(-3)=3, g(−3)=3, g'(-3)=2, calculate the following: (fg)′(−3)= (f/g)′(−3)=…

A: we have to calculate the following: (fg)′(−3)=(f/g)′(−3)=(g/f)′(−3)=

Q: A ship is moving at a speed of 15 km/h parallel to a straight shoreline. The ship is 8 km from shore…

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Q: Given the graphs of f(z) and g(z) below, find the composition of functions f(g(0)) g(x) 18 16 14/ 12…

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Q: A railroad bridge in one city has a low clearance for trucks. An engineer standing 23 ft away…

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Q: Find an equation of the parabola with vertex (2,-4) and focus (2, -7). 5 믐

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Q: Write the function, y = |x| after the following transformations: 1) Reflect the function about the…

A: write the function after the transformation

Q: -3 -110 lim g(x) = x→2- lim g(x) →2+ = lim g(x) = = x→2

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Q: 6) Draw the graph of a function f such that f (2) = 3, f (4) = 7, the function is decreasing on the…

A: Given 1. f2=3 2. f4=7 3. Decreasing in the interval -∞, 2 and 4, ∞ 4. Increasing on the interval 2,…

Q: 5) For the function f(x)=3√2(x-5)+8 , state the domain and range of f(x) and f'(x).

A: Let's find domain and range of given function.

Q: Solve the differential equation by appropriate Substitution dy ах x + 3y 3x+y __(a) 2 2 b) x dy = y…

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Q: Check here for instructional material to complete this problem. Find the slope of the line shown on…

A: The graph of the line is  To evaluate: The value of the slope of the line.

Q: Find the derivative of f(x) = 2x³log3(2x5-9). O O a.) b.) c.) d.) ƒ'(x) = · 16x7 (2x5-9)In3 f'(x) =…

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Q: Check here for instructional material to complete this problem. Graph y = 1 7x x+4.

A: To graph, y=-(1/4)x+4

Q: 9. S 3 4*+¹ +2* + 2x) dx

A: ∫134x+1+2xdx

Q: Find the equation of the normal line to the curves at the point of tangency, if given. 1.…

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Q: f(x) = b-2x 6 x-b if x < -1 if x ≥ -1. Find the two values of b for which f is a continuous function…

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Q: Given the point in polar coordinates 3.7, Part: 0/2 Part 1 of 2 find two other polar coordinate…

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Q: Kindly answer 6 and 7

A: Need to find out that the given differential equation is exact or not.

Q: Prove that a bounded monotonic sequence is convergent

A: We have to prove that bounded monotonic sequence is convergent.

Q: Check here for instructional material to complete this problem. Find the approximate slope of the…

A: Given query is to find the slope of the line and determine whether it's increasing or decreasing.

Q: f(x)=x^3(x+3) *differentiate the function

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Q: In the figure, the equation of the solid parabola is y=x²-6 and the equation of the dashed line is…

A: Given data:- The equation of a solid parabola, y=x2-6  The equation of the dashed line,  y=5x

Q: How can you find the slope of a line which passes through two points with only the given…

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Q: If z = (x + y)ey and x = 7t and y = 1- t², find the following derivative using the chain rule. Enter…

A: Here we have to find the derivative.

Q: Find the values that satisfy each variable through the Gaussian or Gaussian Jordan Elimination…

A: We have to find the values using Gaussian or Gauss Jordan Elimination Method.

Q: General Direction: • Evaluate the limit of the following transcendental functions using TABLE OF…

A: limx→ -142x

Q: After a hurricane, a homeowner examines trees on his property for damage. He thinks a 22-ft palm…

A: Given : 22ft plam tress is leaning  slightly from it's vertical

Q: ว | 2 dx น x-9

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Q: Find the slope of the line passing through the pair of points or state that the slope is undefined.…

A: Our Aim is to find the slope of the line passing through the pair of points(-4,3) and (2,2). Further…