valuate the following definite integral. 0 1 30 x² - - 25 Find the partial fraction decomposition of the integrand. 30 dx 140. dx= ²²-25 30 Evaluate the definite integral. dx dx = -25 (Type an exact answer.)

Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

Q: Consider the following functions. f(x) = X Find (fog)(x). g(x) Find (gof)(x). = X X + 9 Find the…

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Q: A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: Find the X-intercepts (x,y) and y-intercept (x,y) and the vertical and horizontal asymptotes.…

A: To use the given graph to find the answer of the given question.

Q: Find the exact area of the region bounded by 2y = 4√√x, y = 4, and 2y + 2x = 6

A: Here we have to find the area of the region.

Q: A manufacturer can produce 4320 cell phones when a dollars is spent on labor and y dollars is spent…

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Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9 [(u - 2) du Submit…

A: Topic:- application of integration

Q: (i) Solve the following triangle. (You may need a calculator) C A 45° 105° N B

A: As per the guidelines, we must answer only one of the multiple questions given. Therefore, I answer…

Q: = { x + 15 X C(x) = if x < 100 if x ≥ 100

A: Topic:- function

Q: Answer all of the questions below about the function f(x) graphed below when x = 5. 8 8 f -10…

A: Given Graph:-

Q: 3.4k Σ Evaluate 7k

A: Given ∑k=3∞3.4k7k

Q: 6. Find the functions whose equations in factored form have a factor that is cubed. These functions…

A: see below the answer and explanation

Q: y(x tan x + In y) dx + tan x dy = 0.

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Q: What is the equation of the tangent line to y=−2x^3−x^2+4x+3 at x=3? Write the tangent line in…

A: We have to find the equation of tangent line.

Q: 225 ft ☐☐ X A building that is 225 feet tall casts a shadow of various lengths as the day goes by.…

A: Topic- Application of derivatives

Q: There are only two solutions to the trig equation sin =1. a) True Ob) False c) It depends on the…

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Q: 3 2 -1 2 we rational function f(x) = 1 3 Q 20 2.5r2 +4 > identify the int

A: Topic:- calculus       Definition:- If the second derivative of a function is negative on some…

Q: 1 a 3 2 1 a 1 To find the blue shaded area above, we would calculate: b Where: f(x)dx = area 1 2 3 4…

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Q: Solve the differential equation (x+3)−¹ cos (y) dx - [sin (y) In |5x + 15|-y-¹] dy = 0 cos (y) dx a.…

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Q: U V U a) f(x) = sin x The trigonometric function pictured here is b) f(x) = csc x O c) f(x) = sec x…

A: we need to find which trigonometry function has the following graph

Q: cos² xy' = (1 + y²)

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Q: Which of the following represents a possible equation for a sinusoidal function with an amplitude of…

A: answer is in next step. please give a like!!

Q: Find the area of the surface. The part of the plane 3x+2y+z=6 that lies inside the cylinder x² + y²…

A: Since, the equation of the cylinder is x2+y2=4 and  3x+2y+z=6⇒z=6-3x-2yParameterize the surface of…

Q: 3. State the components of a unit vector that is perpendicular to the vector = (5,2,−1).

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Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: 6) Line y=x between x = 0 and x = 1 is rotating around the x - axis. (It forms a cone). Calculate a)…

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Q: The graph of y=f(x) is shown below. Find the values of f(x) for x=0,x=3 and x=6

A: Here we have to find the values of f(x).

Q: Use the graph of the function to estimate the local maximum and the local minimum of the function.…

A: We have to use the graph of the function to estimate the local maximum and the local minimum of the…

Q: The function f(x) has a domain of [-9, 9] and is plotted below such that the porti of the graph on…

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Q: Write an equation of the form y = mx + b for the line in the following graph. [Hint: Either find the…

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Q: ex 1₁-0² (1 - e²x) a. 3 b. C. ex VI d. √1 G ex ex 3 2 5 ² ( + 2 1-e(2x) 2 5 dx e2x In 1-e2|+C e2 + C…

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Q: Use the matrices below to perform matrix multiplication. B= 37 4 -9 0 12 If the operation is…

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Q: Find the difference quotient f(x+h)-f(x) for f(x) = x² - 4x. h

A: Here is the solution:

Q: -5 -4 -3 -2 -1 5 4 3+ 2+ 1+ -2- -3+ -4 -5+ ܐ 2 3 4 5

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Differentiate the fol y = (sin x)(lnx) a)

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Q: You have an investment of $22,400.00 that you want to double in 11 years. If interest is compounded…

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Q: VIBDIC he following DES. to E visbiol

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Q: - TT V(s) ³3² В where s denotes the length of the edge of the cube. Find ß. = $3

A: Given Vs=β-πβs3

Q: intervals

A: A function is increasing if when y is increasing with respect to x ot vice versa. Hence, Given…

Q: Consider the function f(x) = r? – 5 +4 x + 1 a. Find the first derivative. f'(x) = b. List any…

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Q: Given that f(x) = x²h(x) h(-1) = 4 h' (1) 7 = Calculate f'( − 1).

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Q: Question 4 Use Laplace transforms to solve the differential equation: d²x di 2 + 4x = cos(21) where…

A: Topic:- application of integration and differential equations

Q: ΣΠ n=1 a. 1+4+1 6n 61 5 b. 41 5 is equal to c. The series diverges. d. 66 5

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Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (5 cos t,…

A: Given, r(t)=5 cos t, -3t, 5sin t

Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: Which of the following is the correct limit definition for the derivative of g(x) = x² + x? O (x+h)²…

A: We have given function  gx=x2+x gx+h=x+h2+x+h Derivative of g(x) is given as  g'x=limh→0gx+h-gxh…