Evaluate the integral. S* con5 8x dx n/2 O-2 15 15

Q: Find numbers a and b, or k, so that f is continuous at every point. 3x+ 9, if x<-6 f(x) = { kx+ 6, i...

A: Hair we are given that the function is continuous at every point. we use the concept of limit for fi...

Q: *Problems Involving Continuity A. Tell whether each given function has a solution on the indicated c...

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Q: Determine the equation of the curve whose tangent line at any point (x,y) is e- sin x and passes thr...

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Q: VI– 2e* dx

A: Given that a integration and we solve the solution of this integration by using general property of ...

Q: Function Type Differential Operator AxN + BxN-1+ .+C DN+1 AxNeax (D - a)N+1 cos(Bx) or sin(Bx) (D? +...

A: Solution

Q: Evaluate the integral. s'a In óx dx 219.01 190.21 187.01 O -61.21

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Q: 15. A particle moves along a straight line and has acceleration given by s"(t) = 5t + 3. Its initial...

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. S 1, 0sx s 1 x > 1 ...

A: Given that dydx+y=fx  , y0=1  fx=1  ,0≤x≤1-1    x&gt;1Solution:When 0≤x≤1dydx+y=1 this is the linear...

Q: Given a function whose graph is shown below. 1 0.5 -5 -4 1 2 -0.5사 -1.5 Determine lim f(x). r--1

A: We have the find the limit of f(x) at x = -1 using the graph of f(x).

Q: Identify the type of generalized integral +00 fx'e* dx- and in continuity (if converging) to be calc...

A: According to question,Given Integral,Let I= ∫0+∞ x2ex3 dx

Q: Which of the following is not in the domain of cot(x)? Select all correct answers. Select all that a...

A: We can answer the question as below.

Q: Evaluate the integral. x+ 10 dx x+2

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Q: 16x2 - 25 -da Evaluate the integral: 23 (A) Which trig substitution is correct for this integral? O ...

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Q: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, ...

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Q: 1 Find the derivative of 24 – 3x² +5 글(21-3교2 + 5)글 (4z3 - 6z) 글 (21-3교2 + 5)굴 This function is not ...

A: We can take logarithmic to solve it easily.

Q: d(tan (1)) d(tan x) – 2 for x="% and y = 1. Find the dx using the rule we tan x, dx arned in class f...

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Q: Find the inverse Laplace Transform for Cari Songsangan Tranformasi Laplace untuk 1+(s-2)2 F(s) =5-2)...

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Q: Forms of Summation Notation 6. Square of the sum of variables: Ex; =(x, +x, +...+x,)? Example Evalua...

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Q: х — 1 x² + 8x + 15

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + 3.4 1 1 + + 5.6 2.3 4.5 (Use symbolic notation and ...

A: Given:-     To find:- S2  S4  S6

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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Q: ghing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 fee...

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Q: 3. The fuel used by a car is defined by f(x)=3x=/80-6x+245. where x is the travelling speed in km/h....

A: The fuel used by the car is given by the function: f(x)=310x2-6x+245 where x is the speed of the car...

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9.

A: Given, We have to find the area enclosed by the x-axis and the curve y=-x2+9.  

Q: K石Xuts

A: ∫ Sin-1 x dx   ....(1) Using integration by parts ∫ f1(x)*f2(x) dx = f1(x)∫f2(x)dx-∫[d/dx(f1(x)*∫f2(...

Q: Find or evaluate the integral using an appropriate trigonometric substitution. +3 x2 dx 4 + C

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Q: Test the series below for convergence using the ratio test. n+ 2 24n +1 n=1 The limit of the ratio t...

A: Given: ∑n=1∞ n+224n+1where f(n)= n+224n+1Ratio test : l=limn→∞ an+1anif l&lt;1 then the series is co...

Q: The half-life of cesium-137 is approximately 30 years. If an artifact initially contains 100 g of ce...

A:  decay constant k=ln2half life

Q: cos(2x)81-x (x*+1) Given f (x) = Use logarithmic differentiation to find the derivative of the funct...

A: According to question,Given function,fx = cos2x81-x4x2 + 1

Q: What is the derivative of the following function

A: Given that: 1. h(y)=y1-ey2. f(t)=1+5tln(t)

Q: Calculate and at the points (7,41, 1) and (7,41, –1), where z is defined implicity by the equation z...

A: Given the equation z4 + z2x2 - y - 9 = 0

Q: Find the number(s) 6 such thát the average value of f(z) = 6x² – 26x + 32 on the interval [0, 6] is ...

A: Given that: f(x)=6x2-26x+32on [0, b].Average value is 11 on [0, b]

Q: Given the geometric sequence: 36, 120, 400, ... Find an explicit formula for an, where the first ter...

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Q: Given the differential equation y" - 8y' + 16y = 5x? e4* (1) Find the combined differential operator...

A: First I have written the given differential equation into operator form and then find the auxiliary ...

Q: If a cup of coffee has temperature 94°C in a room where the ambient air temperature is 18*C, then, a...

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Q: 2. Summation of a constant: E,=c, +c, +c3 +...+ c, = nc %3D Example Evaluate the following summation...

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Q: The table below shows the cost, C, of selling x cups of coffee per day from a cart. Determine if the...

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Q: 5. A wooden block is made as shown in the diagram. The ends are right-angled triangles having sides ...

A: Given Total surface area = 7.200 cm2

Q: V(x) = In(sin(x) – cot(x))

A: Use the formula of derivative of composition of functions

Q: The temperatue of a town t months after January can be estimated by the function f(t) = – 28 cos( + ...

A: The solution can be seen below.

Q: If labor (x) costs $235 per unit, materials (y) cost $169 per unit, and capital (z) costs $60 per un...

A: Given that: Labour costs $235 per unitMaterials y cost $169 per unitCapital z costs $60 per unit.

Q: Differentiate the following functions using the limit method: 1) y = 7x - 3x" +x– 10 2) y = ;r - 8x ...

A: We will use limit definition to find derivatives of given function. Since , we know that f'(x)=limh→...

Q: n (n+1) (2n +1) 2. Find the sum (k+4)2, hint use use this formula and subtract out the 1, 2 ,3, and ...

A: Explanation of the answer is as follows

Q: Determine the equation of the curve whose tangent line at any point (x,y) is e* – sin x and passes t...

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Q: Sx V1 – x² dx 3.

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Q: Find the center of mass of a thin plate of covering the region between the x-axis and the curve y = ...

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Q: Compute f' (x) using the limit definition. f (x) = 1 – 15x-1 (Use symbolic notation and fractions wh...

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Q: From the graph of f, indicate the intervals on which f is continuous. 2 4 -8

A: The graph of a function f is said to be continuous in an interval if the graph runs continuously wit...

Q: 2 2 -x+2x- 2, x>0

A: