The population of a certain species is given by N = 127 × 1.06t, where t is measured in years. What is the initial population? By what percentage does the population grow each year?

Q: Using an appropriate substitution, 3 the integral S dx equals: /1-4 (х-1)2

A: Here we have to evaluate I=∫31-4(x-1)2dx

Q: 2. * S 4 (;- e-²) cos (e-2 + Inz) dz 4 sin (e-z + In z) + C A C sin (e-Z + In z) + C B 4 sin (; - e-...

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Q: The solution of the non-exact differential equation (x*e +5dy + (1 +2x²e")dx = 0 is: O x^2 e*y+Inlyx...

A: To determine the solution of the following non‐exact differential equation.x3ey+xydy+1+2x2eydx=0

Q: 102 - Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = a...

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Q: By completing the square, dx the integral S equals: 2x2+8x+10 tan-1(x + 2) + C : tan-1(x – 2) + C th...

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Q: e2 6. - dx -Find 1

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Q: 3. If the sum of two numbers is C, find the minimum value of the sum of their squares.

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Q: g3 (*° – 2x² + 1)dx 9. Evaluate the definite integrals (give exact answers): •3 a) | (2x+3)(x – 5)dx...

A: Given that, There are two integral given, a). ∫23(2x+3)(x-5)dx b). ∫121x3(x3-2x2+1)dx We have to fin...

Q: 2udu = 3 u? – (u²)?

A:

Q: Which of the following best describes the function below? S (x) ={** if.rso |-r² if 0 <.x A. Continu...

A: To find out the correct statement. 

Q: Find the values of a and b if the tangent to y = ax² + bx at (1,5) has a slope of 8.

A: We can find the value of a and b as below

Q: Find the total area between y = -x2 - 2x and the x-axis for -3 sxS2.

A: The objective is to find the total area.

Q: i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that se...

A: We know sequence is convergent when limit of sequence is finite

Q: Question 30 Determine the second derivative of 2x³ + y²= 1 – 4 y A 6x ( y + 2)-! - 9xª ( y + 2 ) -3 ...

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Q: Find the global maximum of the function f (x) 1+ x? on the interval (-0, 0) Write DNE is there is no...

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Q: Te* sin( –4x)dx

A: Find your answer below 

Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above th...

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Q: (C) Desoibe the relationship between the graphs. The graphs of fand are reflections of cach other ac...

A: solution:-f(x)=x3/7(a)y=f(x)=x3/7x=y7/3hence,f-1(x)=x7/3 (b) Graph

Q: And the Inverse function ofr over the glven Interval. Describe the relationship between the graphs. ...

A: f(x)=xx2-9y=xx2-9x2y-x-9y=0(Quadratic equation):comparing with:ax2+bx+c=0roots are:-b±b2-4ac2ahere, ...

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: For f dw ,w = w-wa O w = u^(1/3) O w = u^3 %3D O w = u^(2/3) w = u O O

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Q: Consider the following function and express the relationship between a small change in x and the cor...

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Q: Current Attempt in Progress Use cylindrical shells to find the volume of the solid generated when th...

A: Here, the region is bounded by the curves y=3x-14,y=-3x+4,x=4 is as shown:

Q: 4. f(x)= 2x - 24.x 5. f(x) = 3x 3 -9 6. f(x) = 4x³ +12x? -96x

A: Let's find. 

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: To find out the distance from point P to line AB. 

Q: Find the arclength of y = 2x/2 on 1 < x < 3

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Q: (y-Vx² +y² )dx – xdy = 0 Solve When: x= 0, y =1

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Q: Using tabular integration, the integral St"(-2x² + 4x) cos(2x) dx equals: 3Tt 2 – 2 - -1+ 2 the abov...

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Q: A. Consider the function whose graph is shown below. Determine if the function is continuous at the ...

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Q: Rewrite the following integral using substitution: s8 (1+3x)?dx

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Q: Determine if the integral is convergent or divergent. Evaluate the integral if it is convergent. Sup...

A: To solve the following integral

Q: The derivative of the function y = In is: tan x.

A: Given query is to find the derivative if the expression.

Q: Consider the points A(3,-3, 3), B(4, -5,0), C(-3,-4,0), and D(6, 2, -6). (a) Find the volume of the ...

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Q: 3r-4x+1 if x + 1 3. Given the graph of the function f(x) = complete the table. エー1 if x = 1' Differe...

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Q: DÒ NOT include spaces in between characters. * Given F(x)= f(x)g(x) and f(2) = -3, f'(2) = 4, g(2) =...

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Q: Determine whether the function represented by each graph is continuous or not at the given interval....

A: A function is continuous in an interval if there is no break in its graph over that interval and it ...

Q: https://www.webassign.net/cgi-perl/symimage.cgi?expr=n%20%3D%20f%28t%29%20%3D%20a%2F%281%2Bbe%5E%28-...

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Q: Which of the following functions form a particular solution of the differential equation y"+y = sinx...

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Q: Using the method of substitution, b. I : x2 /9x + 7 dx f(u) du %3| a where u = du dx a = and f(u) = ...

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Q: If f(x) 3 cot lr+ 4, then find the value of f'(-1) is > 8 m IN O O

A: Solve the function

Q: 2x if x 2

A: This is a problem of limit and continuity. Function is called as continues if it's left and right li...

Q: 17. If y = tx, where t is the parameter, what are the parametric equations of the curve x' + y' = 8?...

A: solution:-y=txx3+y3=8x3+tx3=8x31+t3=8x3=81+t3x=21+t33

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: View Policies Current Attempt in Progress Find the area of the shaded region. The image is not to sc...

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Q: Consider the function f(x)=12x^5 + 60x^4 − 100x^3 + 7. For this function there are four important in...

A: Given problem:- Consider the function f(x)=12x5 + 60x4 − 100x3 + 7. For this function there are four...

Q: Find the volume of the solid obtained by rotating the region bounded by y = x , y = 0, a about the y...

A: Given query is to find the volume finthe solid generated.

Q: Which integral would represent the area shown below? The function is f(x) = -x³ + 3. %3D 3 2- 1- 0.5...

A: Given query is to find the area of the shaded region.

Q: From the following results, determine whether the function 2x +9, r 9 f(x) = 6. is continuous at = ...

A: Solve for the continuity for the function

Q: If f(x) = 7 cot-l+ 5, then find the value of f'(-6) is -5 37 -6 37 O 00 O 7 37 O -7 37

A: Topic:- application of derivatives

Q: 5. f(x) = S2e* + 1 if x # 0 0 if x = 0 at x = 0

A: