Calculus Question

Q: Unit tangent vectors at a point Find the unit tangent vector at the given value of t for the followi...

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Q: What are the orders of the equations in the given problem? Are theylinear or nonlinear?   General so...

A: Answer(a): The given differential equation is: y '(t) = 5 cos t + 6 sin 3t. To find the general solu...

Q: Solve by using Cramer's rule: z+ 3x = 1 y + x - z = 2 X – y = 3

A: Cramer's rule in brief: find the determinant of the matrix formed by the coefficients of variables ...

Q: Evaluate the integral.

A: Consider the following integral: ∫csc44xdx Substitute 4x=u→4dx=du→dx=14du in the above integral: ∫cs...

Q: Plan A has a monthly fee of $15 with a charge of $0.08 per text. Plan Bhas a monthly fee of $3 with ...

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Q: "If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at whi...

A: Surface area =4πr2 surface area=π2r2As we know DiameterD=2rsurface area=πD2   

Q: Sketch the graph of the equation y − 1 = 3(x + 4)

A: y-1=3(x+4) We need to plot the graph of the equation.

Q: Rewrite the equation y = 100(4.6)x in terms of base e. Express the answer in terms of a natural loga...

A: y = 100(4.6)x     Let 4.6 = ez    => ez = 4.6     => ln ez = ln 4.6    => z*ln e = ln 4.6  ...

Q: 10-

A: Consider the function; y=5x-72x+1

Q: If f(x)=17x+11f(x)=17x+11, find the slope of the secant line between the values of x1=1x1=1 and x2=−...

A: Given fx=17x+11 x1=1,x2=-1    

Q: Show that the function f(x) = |x - 6| is not differentiableat 6. Find a formula for and sketch its g...

A: Consider the given function: fx=x-6 Here, the objective is to show that the given function is not di...

Q: 2x+1, x <0 Evaluate the function x) = at 5) %3D 2x+ 2, x 2 0

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Q: Set u = x^2. Note that a “special skill” is needed here - solve dx.

A: The given integral is ∫1xx4-4dx. Let u=x4-4. Then, du=4x3 dx. Apply the substitutions and evaluate t...

Q: 2, Differentiate the following functions. DO NOT USE PRODUCT OR QUOTIENT RULES. SHOW ALL WORK/EXPLAI...

A: a. f(x)=e6+5x4+6e Differentiating f(x) with respect to x using power rule of differentiation ddx(xn)...

Q: Find the term indicated in the expansion: (x + 2y)6; third term

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Q: If g(z) -f(x), complete each of the following. %3D a. If f(4.5) = 65, then g(4.5) Preview %3D %3D b....

A: "As per authoring guidelines, the first three sub-parts of the question is answered. Please repost t...

Q: Let f(x) = 2x2 - x - 1 and g(x) = 4x - 1.Find (f ∘ g)(x).

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Q: Solve the logarithmic equation log3(x + 4) = -3. Be sure to reject any value of x that is not in the...

A: Given log3x+4=-3

Q: Derivatives Evaluate the following derivatives.

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Q: Simplify: k(k + 1)(2k + 1)/6 + (k + 1)2.

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Q: Evaluate the following limits and justify each step lim x 5 (2x2 -3x +4)

A: limx→52x2-3x+4 We need to find the 

Q: Determine equation of tangent line to the curve at given point. a) f (x)= 3x² - 5x +2 at x = -3 %3D

A: Equation of straight line is given by y = mx + c ; where m is the slope c is the y intercept. For ta...

Q: Can you evaluate the limit

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Q: Find T, N, and k for the space curves r(t) = (cosh t)i - (sinh t)j + tk

A: Let the given space curve is r(t)=(cosh t)i-(sinh t)j+tk   To determine: The values of the unit tang...

Q: Use the Intermediate Value Theorem to show that sin x x2 – x has a solution on the interval (1, 2).

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Q: Find the function value, if possible. (If an answer is undefined, enter UNDEFINED.) f(x) = 3x − 3  ...

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Q: For the function  y = 6x2 + 5x + 1,  at the point  x = 5,  find the following. (a) the slope of the ...

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Q: Exercise4 :a) Compute dy when: dxx = θ + cosθ ;y = θ − sinθ1 b) Compute d2y when: dx2x = θ + cosθ ; ...

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Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high t...

A: Let temperature can be modeled as y=A+Bsinwt So maximum value y = A+B=105      ....(1) Minimum Value...

Q: Use the guidelines of the section to make a complete graph of ƒ.

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Q: What can be said about functions whose derivatives are constant? Give reasons for your answer.

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is parallel to the line y...

A: Given curve is y=2x3-3x2-12x+20 Given line is y=2-12x=-12x+2  Slope of the given line is -12. Differ...

Q: Simplify 24x3y5 / 32x7y-9

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Q: Describe the pattern in the exponents on b in the expansion of (a + b)n.

A: We have to describe the pattern in the exponents on b in the expansion of (a + b)n.

Q: An object moves in simple harmonic motion described by d = 10sin 3ᴫt/4, where t is measured in secon...

A: Explanation: We know that the standard equation of simple harmonic motion is described by:          ...

Q: 29. In each case, determine whether or not the point lies on the line. If itdoes not, give an equati...

A: The line passes through the point B=3,-3,1 and has direction vector v→=4,4,1. Another vector in the ...