Find the area of the triangle whose vertices are given below. A(- 5,3) B(2,– 5) C(10,- 5) The area of triangle ABC is square units. (Simplify your answer.)

Q: J(x+h)-f (x) h 4x+9x+5 Problem #1: Using lim, Find the slope of the tangent line y = 3x-8 at x = -1.

A: Given: y=4x3+9x+53x−8 Let f(x) =y=4x3+9x+53x−8 We know that f'x=limh→0 f(x+h)−f(x)h Now slope of the…

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Q: following functions fo - VE+3 and glo) = Find the formula for eXx) and simplify your answer. Then…

A: For f(x)=x+3 and g(x)=x+42, Our Aim is to find the formula forg∘fx and domain for g∘fx.

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Q: Evaluate the difference quotient fla+k) - fla) for the function fx) = 5x. %3D 1 5h

A: We can find the difference quotient

Q: Let C(x) be the cost, in dollars, to produce x gallons of gelato. What is the meaning of C'(5) = 4.5…

A: Given, C(x) is the cost in dollars. x is the gallons of gelato.

Q: 5. L.V4– 2x dx dx 5x+2 6.

A: Topic = Integration

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A: We ahve to find the interval of convergence of the series.…

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Q: 4. y = e 2coscns (2x) 5. y = e

A: Here we have to find the derivative of question number 4 &amp;5

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Q: The following series is convergent: 3n 2n? – 1 Σ 4 + 5n2 n=1 Select one: True O False

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Q: 1. Find the determinant of the given matrix. 1 0 4 -6 2 5 3 -1 2 3 2 1 -2 31 det A

A: Given :A=104-62503-123521-23

Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 1+ +(…

A: Use geometric series to check the convergence

Q: 5) Find the area enclosed by the circle r = 3 cos 0 and the cardioid r =1 + cos 0.

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Q: Question 2. (a) ( Evaluate the triple integral z dV, where E E = {(x,y,z):0<x<2, 0<y<2, 0Sz<3). (b)…

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Q: Find the slope of the tangent line to the curve given by x + y° = 2 at the point (1, 1) -1 O 1

A: find the slope of the tangent to the curve x5+y5=2 at (1,1)   d(xn)dx=nxn-1

Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

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A: This is a problem related to area calculation by integration. Based on the given graph we will…

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Q: find ganeral From of taylak Seriesot FOA-In(3t4xl, about X-0 %3D

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Q: Sketch the graph of a function f with domain [1, 5] satisfying all the following conditions: •…

A: This question can be solved by the concept of nature of graphs.

Q: Let R=[0,1]x[0,1]. хуз dA= 41x2+1 R

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Q: Directions: Read and understand each problem carefully. Solve for what is asked in each problem and…

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Q: 20) dx 1 19 A) 6. B)= D) 9/2

A: I=∫12 t8-t4t6 dt=∫12 t2-t-2 dtformula: ∫ xn dx=xn+1n+1+C  =t33-t-1-112  =t33+1t12    =83-13+12-1…

Q: Given r= (-3,10) and s= (12,-7), find a- r+s b- s-r.

A: Here we have to find the given operation.

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Q: Use the numeric integration feature on your calculator to find the integral. 4. 27) A) 0.88623 B)…

A: We can find the answer as below.

Q: Find the area under the graph of the function over the interval given. 32) y =x2 +1; [0, 1] A) D)를…

A: Given :y=x2+1   0,1

Q: The series 33n-54-1-2n is n=1 Select one: а. is convergent but not a geometric series. O b. is…

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Q: 12 – r|, 2. Suppose f(r) = {0, if a > 2 if r = 2 14 – 22|, if r < 2. (a) Find lim f (x). z+2+ (b)…

A: a)limx→2+ f(x)=limx→2+ 2-x=limx→2+ 2-2 =0b)limx→2-  f(x)=limx→2- 4-x2=limx→2- 4-4 =0

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Q: 16. (ho f)(x) (A) VAr – 1 (C) 4r² +1– 1 (B) 2r – 1 (D) 0 17. (fo h)(1) (A) VAr – 1 (C) 4r2 – 1 (В)…

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Q: 32

A: We need to use the knowledge of binomial theorem to solve this problem.

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Q: So 0 cos r0 do

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Q: Evaluate the following limits or explain why the limit does not exist. (c) lim as x approaches 0 x…

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Q: (a) Use the Second Derivative Test to find the local extreme values of the function

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Q: Consider the two series: 2n + 3 (а) n² In n n=1 00 1+ (n – 1)! (b) E n! n=1 Which of the following…

A: 1) Hee, note that the first series first term it self a infinity.

Q: Graph the following function Function المعادلة الرئيسية у3- cos (x) y=A cos (Bx+C)+D A= y B= C= D%=…

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Q: Suppose that a function f(x) satisfies the following properties, together with the table of signs…

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Q: 6. S (1 + 3æ)*dx

A: