Direction: Read and understand the statement before answer. Click "TRUE" if the statement is correct and click "FALSE" if the statement is incorrect. QUESTION: If a function has derivatives from both the right and the left at a point, it is differentiable. Select one: O True False

Q: Tell if the function is continuous at given interval f(x)=; 2x +4 |-2,2]

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Q: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline...

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Q: 4. Homogeneous Diffe rential Equation: (x* +2.xy – 4y² kdx– (x² – 8.xy – 4y² kdy = Use the substitut...

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Q: Find the interval of convergence of Σ (-4)" (x+10)" n! (Use symbolic notation and fractions where ne...

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Q: J Va4 + 1 ‚4

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Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: y = Ce-2 + C2e3*

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Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) = 38.96(...

A: 1. p(t)=38.961.017t, where t=0 corresponds to 2000 Note:    multiple questions are given we are answ...

Q: Exact Diffe rential Equation: x(3xy - 4y' +6) kx + (x³ – 6x²y² -1\dy=0

A: Check firstly it is Exact or Not.

Q: Consider the vector field F Evaluate |F. dī along the curve C: 7(t) = tỉ +t°j, 0 <t < 2

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to I (- x - 2x + 12x + 4x...

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Q: Find the x-value(s) where the graph does not have a derivative. The x-value(s) where the function do...

A: Given: There is a sharp point at x = 1. So, the function is not differentiable at x = 0.

Q: Evaluate the TV100-x²dx

A: Topic = Integration

Q: The equation of a family of parabolas with axis parallel to the y-axis is

A: We will find the equation of family of parabolas with axis parallel to the y-axis .Below find the ge...

Q: Which of the following is equivalent to sec B(tan?B+1) for all values of ß for which sec B(tan²B+1) ...

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Q: A spherical iron ball 8 in. in diameter is coated with a layer of ice of uniform thickness. If the i...

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Q: A potato is dropped from a height of 70 feet. Its height above the ground t seconds later is given b...

A: Put S=0 which means potato touch the groun so that height from groun is 0.

Q: Let f(x, y) = 8x + 2y2, r(t) = (cos(t), sin(t)). Use the Chain Rule to calculate f(r(t)). !! dt r(r(...

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Q: Solve for x. 8e^(-7x)=2

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Q: 3. y'-5y=x²e* – xe*

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Q: x3 00 dx = (x* +4)2 0,

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Q: dy dt II

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Q: Approximate dx using the midpoint rule with four subdivisions to four decimal places. J2 In(x) The a...

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Q: If h(x) = V5 + 4f(x), where f(1) = 5 and f'(1) = 2, find h'(1). h'(1) =

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Q: point 4 m above ground level with an initial velocity of 21.5 m/s is h = 4 + 21.5t – 4.9t2 after t s...

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Q: Find for the following function. dx 3- cos X y = 4 + coS X

A: follow next styep

Q: 4. What is the equation of the tangent line to y = sin(sin(x)) at the point (T,0)

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Q: 1. /* dx x3 + x

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Q: Let y=f(x) be the solution to the differential equation dydx=x−y−1dydx=x−y−1 with the initial condit...

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Q: find all of the critical points and local maximums and minimums of each function. (a) f(x) = 1+ x2 '...

A: Note: Since multiple questions are asked, I am answering the first question.please repost other ques...

Q: 4) Determine whether the improper integral diverges a) fx'e *dx or converges: 1 b) J (7x +1)³ 1

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Q: In x to show that In a loga x = Use the change of base formula loga x = x In a loga x dx dx In a In ...

A: topic - derivative of logarithmic function

Q: 5. Exact Diffe re ntial Equation: x(3xy – 4y' +6}dx+(x' – 6x² y² -1dy =0

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Q: find all of the critical points and local maximums and minimums of each function. (d) f(x) = |æ+ 5|....

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Q: There is a removable discontinuity at x = 1 and f(1) = 4

A: we have to sketch the graph .

Q: A graphing calculator is recommended. The motion of a spring that is subject to a frictional force o...

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Q: If a tank holds 2000 gallons of water, which drains from the bottom of the tank in 40 minutes, then ...

A: This question can be solved by applying the concept of rate of change of quantities.

Q: 9. lim e 10. lim e sin 6x 11. lim 5*+6 12. lim

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Q: Consider the initial value problem and find the solution for y''+4ay'+(4a²y+4y)=0 and y(0)=-2, y'(0)...

A: Solution: y''+4ay'+(4a²y+4y)=0 and y(0)=-2, y'(0)=-1.

Q: 10. Determine the intervals for which the functions are continuous. (c) f(0) = -2 cos 0+ sin 0 (a) g...

A: Every polynomial function is always continuous on Real number. Sum of two continuous function is alw...

Q: A particle moves along a straight line and its position at time t is given by s(t) = 2t – 21t + 36t ...

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Q: 2. y"-7y'=(2x-1)sin 2x

A: Given,y" - 7y' = (2x-1) sin2xNow substituting the value:y" = D2yy' = DyD2y - 7Dy = (2x-1) sin2xD2y -...

Q: Find the following values for f(x) = sin =). (Be sure your computing device is set to RADIAN mode) 0...

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Q: Which of the following is equivalent to tan 0(sec 0 – 1)(sec 0 + 1) for all values of 0 for which ta...

A: NOTE: Refresh your page if you can't see any equations. . use the formula 

Q: Which expression is equivalent to sec a(1 – cos?a) for all values of a for which sec a(1 – cos²a) is...

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Q: A TV camera is situated 100 m from the site of the Endeavour launch The rocket's elevation t seconds...

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Q: For the cost function C(x)=40+x-1/2x^2 find the marginal average cost when x=2

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Q: A material transmutes 50% of its mass to another element every 10 years due to radioactive decay. Le...

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Q: Ląsudnhlao203=9m] -03P99E90RO[9U3RM7210 Ud8y(l,ome 301 29u 3 ***#!12ngwe gggd 982eh cc d´y The degre...

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Q: Use Simpson's Rule and all the data in the following table to estimate the value of the 20 integral ...

A: Follow the procedure given below.