Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=t+t³ y = 2 + t² t = 1

Q: Answer the following questions for the function f(x)=x√x²+1

A:

Q: (c) State the Fundamental Theorem of Calculus Part II.

A: In this question we have to state the Fundamental Theorem of Calculus Part II.

Q: g(x) dx = (Simplify your answer.) 7 4g(x)dx= 2 (Simplify your answer.) 7 [g(x)-f(x)]dx = (Simplify…

A:

Q: Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 7x - 3x² g(x) = c₁f₁(x) + C₂²₂(x) +…

A:

Q: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0

A: To solve the differential equation.

Q: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and…

A: In this question we have to find the value of b and c.

Q: At which octant will you find (-8, 13, -1/2)?

A:

Q: find the unit vector in the direction of u u=

A: find the unit vector in the direction of u u=<-4,-1,-3>

Q: LI) Prove that (3

A:

Q: 34. dx = x³+4x² + 5x - 1 is given. What is ƒ(1)? A.-7 B.3 C.-2 D. 16 35. Evaluate the integral f(x²…

A: 34) The integration of the integral is f(x)/x2=x3+4x2+5x-1.  35) The given integral is…

Q: Q5: Find dy dx (1) In(x - y) = xy + y³; for the following functions: (2) y = tan³√/cot(7x);

A:

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

A:

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A: Find determinant of coefficient Matrix  Then find delta x ,delta y, delta z

Q: Find the limit. lim X→x ←+ -54 -3 -2 -1 00 O-2 f(x) 00 SIEX) 4 m 2 14 -3 2 3

A:

Q: What is the general solution to y² tan(x) dy = sin(x) dx o y = √3 sin(x) + C o y = -√√3 cos(x) + C o…

A: Here we have to solve the differential equation.

Q: 2. Approximate 64.1 by using linearization and use a calculator to compute the percentage error.

A: Given :64.13

Q: A function is given. f(x) = x³ 3x²; x = 0, x = 10 (a) Determine the net change between the given…

A:

Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t)i + sin(t)j + tk…

A:

Q: Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also,…

A: Please see the below picture for detailed solution .

Q: given the surface revolution x^2+z^2-5y=0 find the equation of its generating curve in the yz-plane…

A:

Q: Sketch the region enclosed by the curves and find its area. Enter the exact answer. Area = y = 2x²y…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the curves 3π y = sin x +…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the curves…

Q: Use the figure below to find the exact value of the trigonometric function of angle A. csc (A) 7 5 A

A: We have to find the exact value of the trignometric angle A, csc(A)=? Since ABC is right triangle,…

Q: Q2/ A. Find the following limits. Answer four only. i. ii. iii. iv. V. lim x1 x-1 4x-x² lim X-4…

A: To evaluate the limit.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here, the given curves are: y=1+2x, y=2+x2

Q: What is 2x2

A: We can answer the question as below.

Q: Use the tabulated values off to evaluate the left and right Riemann sums for n = 10 over the…

A:

Q: 2x + 2 6x³ +5x² - 4x y = 3

A:

Q: Find the limit as x approaches 3 for x²-3x 2x²-5x-3

A:

Q: In a classic video game, balloons travel from left to right along a linear path that passes through…

A: Given equation is :   x-12+y2= 100 ---- equation of circley=3x+7 --------equation of line

Q: ind the definito integral that will computo for the area of the region bounded by y-2 ln x v-0 andy…

A:

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A:

Q: Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be…

A: Solution is given below:

Q: √(3x − 5)(x² + 1)da

A:

Q: Q1/ Answer the following: A. Find the shortest distance between the point A (3, 10) and the line y =…

A: We can find the shortest distance as below.

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A:

Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

Q: Use the remainder theorem to evaluate the polynomial for the given values of x. g(x)=6x³-7x²-36x+42…

A:

Q: The function g is related to one of the parent functions  g(x) = |x − 1| + 5 a.) Identify the parent…

A:

Q: defined on the interval [-5, 7]. a.) f(x) is concave down on the open b.) f(x) is concave up on the…

A: This question can be solved using the concept of point of inflection, critical point and point of…

Q: Question 1 Given the series: 2³-(²3)* Σ5. k=0 k does this series converge or diverge? diverges…

A: The objective of the question is check the converges of series and determine the  sum of series .

Q: What is the general solution to ya dy dx ○ y = ±₁/2. + C 4x In(4) o y = +. o y = o y = + 4x In(4) +…

A:

Q: 1. / (1 + 3x) dx 5 2. / u² (4 + u°) ³ du

A:

Q: Use implicit differentiation for x² + y² O x/y O 5x O-x/y O -5x = 25.

A: To find the derivative.

Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y² ;

A: Find the derivative

Q: (e) Evaluate S 1+7x dx.

A:

Q: S 2 (2 x ² + 1 ) 1²/1 2 dx

A:

Q: Find the Taylor or McLaurin series for the following functions X f(x) = 1 + x², a=0

A:

Q: Researchers at two universities have developed a piecewise function that can be used to estimate the…

A:

Q: 6. Σ(-1)n-1 sin (2) n=1

A: Explanation of the answer is as follows